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                  Starting BigCrush
                  Version: TestU01 1.2.3
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                     Run no 56000
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.23
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.49
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.32
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.71
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.53
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.23
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.03
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.64
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.28
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.31
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 62                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.43
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.89
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.85
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908997
   j =  2                              :            45494
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907612
   j =  2                              :            46191
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 78                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 107                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.35
 p-value of test no 118                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.69
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.20
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.64
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.80
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.16
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.15
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.37
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.81
 p-value of test no 134                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.25
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.57
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.39
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.45
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.60
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.77
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.25
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.53
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.38
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.23
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.86
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.50
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.26
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.72
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.84
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.71
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.61
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.42
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.61
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.98
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.12
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.01
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.18
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.15
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.76
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.61
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.00
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.62
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.06
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.81
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.99
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 183                :    0.02
 
 Sample variance                       :    2.64
 p-value of test no 184                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.12
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.85
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.86
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.33
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.82
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.64
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.13
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.14
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.40
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.98
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.41
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999995351
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.14
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000129058
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 236                :    0.9923
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.061
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:55.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83263509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56001
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9931
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.57
 p-value of test no 47                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.53
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.09
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.76
 p-value of test no 52                 :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.75
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.90
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.11
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.64
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.87
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 63                 :    0.9902
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.16
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.99
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.18
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.36
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46488
 p-value of test no 70                 :  2.3e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870488
   j =  1                              :        399907032
   j =  2                              :            46472
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907878
   j =  2                              :            46055
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.99
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.31
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.23
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.79
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.81
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.04
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.00
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.50
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17219.13
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.23
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.58
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.77
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.24
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.62
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.30
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.22
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.81
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.55
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.15
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.13
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.39
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.03
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.65
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.13
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.22
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.60
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.10
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.39
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.08
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.86
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.43
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.16
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.24
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.27
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.08
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.42
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.16
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.66
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 182                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.55
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.63
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.87
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.75
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.04
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.03
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.45
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.31
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.63
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.79
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11545.59
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.71
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000080419
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.24
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999894431
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:00.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84181013.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56002
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.94
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.67
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.26
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.98
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.68
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.31
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.10
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.56
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.62
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.21
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.62
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.97
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.39
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 63                 :    0.9918
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   36.19
 p-value of test no 65                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.73
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.80
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.41
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45460
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869460
   j =  1                              :        399909084
   j =  2                              :            45452
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908388
   j =  2                              :            45803
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
 p-value of test no 91                 :    0.9953
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
 p-value of test no 93                 :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.56
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.38
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.74
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.66
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.85
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.93
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.12
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.71
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17626.75
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.58
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.16
 p-value of test no 147                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.65
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.65
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.59
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.02
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.86
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.15
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.49
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.15
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.24
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.73
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.84
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.73
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.93
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.32
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.41
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.73
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.26
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.88
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.97
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.19
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.91
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.99
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.12
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.25
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.70
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.78
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.95
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.96
 p-value of test no 198                :    0.9985
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.81
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.86
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.39
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.22
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.03
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.88
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.36
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.31
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.72
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.29
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.18
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000175084
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.05
 p-value of test no 233                :  3.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999875018
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:56.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85065749.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56003
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.85
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.10
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.74
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.74
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.57
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.88
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.10
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.06
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.04
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.95
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.92
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908233
   j =  2                              :            45882
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.82
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.56
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.23
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.00
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.88
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.90
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.70
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.97
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.24
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.47
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17325.77
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.44
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.35
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.43
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.21
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.95
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.16
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.38
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.06
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.25
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.75
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.39
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.81
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.43
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.76
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.37
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.79
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.82
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.78
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.20
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.90
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.07
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.77
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.24
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.47
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.12
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.96
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.15
 p-value of test no 178                :    0.9944
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.76
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.73
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.61
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.32
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.28
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.40
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.59
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.51
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.24
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12068.45
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.13
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.22
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999907541
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.38
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000113401
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:18.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86048789.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56004
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.47
 p-value of test no 34                 :  5.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.69
 p-value of test no 41                 :  4.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.63
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.04
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.29
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.42
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  181.95
 p-value of test no 54                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.92
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.35
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.70
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.57
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.53
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.46
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.64
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908425
   j =  2                              :            45780
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46285
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870285
   j =  1                              :        399907433
   j =  2                              :            46279
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.65
 p-value of test no 115                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.59
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.32
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.24
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.04
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.27
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.61
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.67
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.17
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.50
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.38
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.61
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.30
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.67
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.57
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.48
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.54
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.79
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.58
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.17
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.31
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.91
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.67
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.33
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.62
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.92
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.23
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.06
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.25
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.66
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.96
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.05
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.55
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.43
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.59
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.92
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.76
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.66
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.13
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.04
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.63
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.01
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.02
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.40
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.18
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.94
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.96
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.92
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.03
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.68
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.61
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.33
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.44
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.06
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999876926
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.41
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999961220
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:38.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87195669.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56005
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.85
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.04
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.39
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.80
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.60
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.11
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.60
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.19
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.59
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.91
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.42
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.93
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.26
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.71
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.93
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.84
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908552
   j =  2                              :            45718
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908309
   j =  2                              :            45838
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.16
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.68
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.61
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.97
 p-value of test no 125                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 128                :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.88
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.01
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.16
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.39
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.05
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.70
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.07
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.90
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.28
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.10
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.18
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.24
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.49
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.48
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.53
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.56
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.14
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.52
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.32
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.99
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.65
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.46
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  487.85
 p-value of test no 166                :  2.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.79
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.17
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.66
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.61
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.20
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  465.33
 p-value of test no 172                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.05
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.36
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.59
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.93
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 180                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.07
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.09
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.49
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.95
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.27
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.21
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.39
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.24
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.85
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.16
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.86
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.93
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12088.13
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.53
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999955634
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.71
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999856472
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 H (L=10000, r=0)    2.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88080405.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56006
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.61
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.02
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.67
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.52
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.99
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.41
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.59
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.05
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.76
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.69
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.60
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.91
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907649
   j =  2                              :            46171
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908467
   j =  2                              :            45762
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9934
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.02
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.15
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.97
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.30
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.61
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.43
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.20
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17196.51
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.12
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.53
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.45
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.12
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.68
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.40
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.84
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.52
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.59
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.20
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.12
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.34
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.88
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.71
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.52
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.58
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.35
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.98
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.23
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.30
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.99
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.61
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.38
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.49
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.58
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.85
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.32
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.03
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.74
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.77
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.88
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.85
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.23
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.76
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.02
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 220                :  5.3e-4    *****
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.08
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.48
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3928.36
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.22
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.11
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.53
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.71
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999857210
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.93
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000033391
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:36.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89063445.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56007
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7521
 p-value of test no 20                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.65
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.06
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.48
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.65
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.50
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.27
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.94
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.87
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.46
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.17
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.56
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.62
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908098
   j =  2                              :            45948
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908508
   j =  2                              :            45737
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.81
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.19
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.21
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.46
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.95
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.81
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.15
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.31
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17107.50
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.20
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.11
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.99
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.97
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.30
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.24
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.76
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.32
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.62
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.07
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.70
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.93
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.09
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.01
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.91
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.83
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.69
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.21
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.60
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.95
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.13
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.16
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.72
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.31
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.24
 p-value of test no 175                :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.35
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 180                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.35
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.63
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.24
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.72
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.58
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.97
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.61
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.33
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.29
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.97
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.78
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.28
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.22
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999885584
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.37
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999744278
 
 Normal statistic for number of bits   :   -2.02
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.92
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:56.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89980949.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56008
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.92
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.99
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.19
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.18
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.23
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.01
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  295.21
 p-value of test no 54                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.13
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.87
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.52
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.32
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.47
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.71
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.79
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908311
   j =  2                              :            45843
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908408
   j =  2                              :            45793
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 98                 :    0.9901
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.37
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.78
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.25
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.86
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.73
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.98
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.23
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.52
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.13
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17654.01
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.12
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.72
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.40
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.30
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.38
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.92
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.90
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.56
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.87
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.66
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.51
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.91
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.96
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.79
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.70
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.01
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.58
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.43
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.18
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.28
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.87
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.37
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.81
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.43
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.74
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.13
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.84
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.28
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.92
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.70
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.42
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 225                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4658.10
 p-value of test no 226                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.66
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4339.18
 p-value of test no 228                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.66
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12182.44
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.62
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999984992
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.89
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999997730
 
 Normal statistic for number of bits   :  -0.018
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.92e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:06.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91226133.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56009
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.61
 p-value of test no 34                 :  4.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.08
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.63
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.66
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.65
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.97
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.92
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.06
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.49
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.82
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.72
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.92
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.59
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.90
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.17
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908656
   j =  2                              :            45666
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908553
   j =  2                              :            45719
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.75
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.24
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.07
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.00
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.55
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.90
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.37
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.81
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.17
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.65
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17623.56
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.02
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.82
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.75
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.87
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.15
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   64.86
 p-value of test no 151                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.28
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.31
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.03
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.43
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.82
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.89
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.12
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.26
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.29
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.64
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.16
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.00
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.86
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.74
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.20
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.25
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.23
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.07
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.31
 p-value of test no 172                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.23
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.31
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.49
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.14
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.77
 p-value of test no 203                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-5
 p-value of test no 204                : 1 -  1.7e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  256.08
 p-value of test no 207                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.63
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9735.00
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.26
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.69
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.70
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.46
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.45
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.26
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.99
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000002731
 
 Normal statistic for number of bits   :   0.022
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.69
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000048382
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    2.11
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:45.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92274708.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56010
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1222
 p-value of test no 12                 : 1 -  4.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334342
   j =  1                              :        599997556
   j =  2                              :             1222
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.81
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.21
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.88
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.60
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.09
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.81
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.46
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.86
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.96
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.94
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.88
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.99
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.87
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.03
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4858.96
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908155
   j =  2                              :            45915
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908713
   j =  2                              :            45636
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.21
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.29
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.22
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.87
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.87
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.84
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.82
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.36
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.06
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.52
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.08
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.19
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.78
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.02
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.65
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.44
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.29
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.17
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.47
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.17
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.01
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.44
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.48
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.43
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.88
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.76
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.28
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.80
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.52
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.27
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.49
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.38
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.21
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.18
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.46
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.97
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.77
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.58
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.92
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.28
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.36
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.81
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.86
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.39
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.23
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.15
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.78
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999978992
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.87
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999955145
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.93
 
 Sample variance                       :    2.31
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    2.60
 p-value of test no 244                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:48.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  4.8e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93290511.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56011
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    4.28
 p-value of test no 27                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 39                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    3.60
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.79
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.08
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.87
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.27
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.03
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.92
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.89
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.25
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.90
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.13
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.33
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.24
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908162
   j =  2                              :            45913
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907928
   j =  2                              :            46030
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.35
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.01
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.72
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.67
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.47
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.68
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 130                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.81
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.82
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.80
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.55
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.89
 p-value of test no 150                :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.89
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.14
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.58
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.26
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.88
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.32
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.12
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.93
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.98
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.02
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.40
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.39
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.28
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.98
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.75
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.30
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.66
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.37
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.34
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.52
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.50
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.51
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.34
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.55
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.29
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.73
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.69
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.32
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.48
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.74
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.11
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.57
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.10
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.43
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.45
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.58
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.24
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.74
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999977681
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.18
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999889382
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.073
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:01.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94437391.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56012
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 12                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.88
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.85
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.46
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.89
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.29
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.88
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.70
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.24
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.33
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6909.08
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.42
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.15
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.75
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.55
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.97
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908483
   j =  2                              :            45748
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45418
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869418
   j =  1                              :        399909167
   j =  2                              :            45412
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.70
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.52
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.01
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.72
 p-value of test no 123                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.97
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.40
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.29
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.67
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.49
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.13
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.00
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.67
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.68
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.36
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.77
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.45
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.59
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.55
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.57
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.47
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.61
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.62
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.49
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.12
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.95
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.80
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.73
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.95
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.24
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.43
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.52
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.33
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.84
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.61
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.39
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.56
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.10
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.77
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.02
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.66
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.61
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.92
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.87
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.96
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.25
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.38
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.86
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.77
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.42
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.36
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.52
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.09
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.39
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000008395
 
 Normal statistic for number of bits   :   0.066
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.84
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000083203
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:51.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95387663.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56013
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.70
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.24
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.61
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.24
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.18
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.27
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6847.99
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.18
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.55
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.27
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.28
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907803
   j =  2                              :            46094
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908519
   j =  2                              :            45733
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.13
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.80
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.56
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.59
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.04
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.72
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.83
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.57
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.55
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.55
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.49
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.49
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.08
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.11
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.21
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.17
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.40
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.61
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.66
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.70
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.85
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.71
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.60
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.00
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.46
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.92
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.93
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.80
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.82
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.66
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.12
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.62
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.69
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.51
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.88
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.04
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.82
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 214                :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.77
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.010
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.53
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.86
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.83
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4309.27
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.98
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11627.22
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.64
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000113986
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.30
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999927503
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 252                :  6.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.74
 p-value of test no 253                :  3.1e-3
 
 Sample variance                       :    2.69
 p-value of test no 254                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:49.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96337935.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56014
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.12
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.07
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.95
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.69
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.31
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.39
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.79
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.50
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.53
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.14
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.14
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.61
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5180.74
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907926
   j =  2                              :            46034
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908380
   j =  2                              :            45807
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.55
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.26
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.14
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.31
 p-value of test no 123                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.25
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.01
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.92
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.59
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.92
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17646.41
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.93
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.85
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.90
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.89
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.60
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.45
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.62
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.35
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.45
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.44
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.05
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.81
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.42
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.91
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.92
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.92
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.33
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.11
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.19
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.76
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.37
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.93
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  446.56
 p-value of test no 169                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.75
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.44
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.88
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.89
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.67
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.92
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.52
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.12
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.46
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.90
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.11
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.21
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.32
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.13
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.72
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.98
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.35
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.34
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.83
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000064237
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.17
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000201829
 
 Normal statistic for number of bits   :    1.60
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:48.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97681423.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56015
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.67
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.26
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.35
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.26
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.70
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.90
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.31
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.00
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.45
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.37
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.46
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.45
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.83
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.86
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.84
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908321
   j =  2                              :            45835
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907785
   j =  2                              :            46103
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.90
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.55
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.38
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.00
 p-value of test no 122                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.49
 p-value of test no 123                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.61
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.48
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9936
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.71
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.93
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17884.33
 p-value of test no 145                :  7.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.34
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.99
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.06
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.50
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.79
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.84
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.11
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.59
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.14
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.61
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.47
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.59
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.28
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.71
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.38
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.90
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.96
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.77
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.08
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.82
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.99
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.03
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.28
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4820.27
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.32
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.16
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.43
 p-value of test no 196                :  4.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.30
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.91
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
 p-value of test no 208                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10303.59
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.18
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.83
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.18
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.93
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.92
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.05
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11499.14
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.10
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000007606
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.13
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999952007
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.83e-4
 p-value of test no 236                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9930
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:12.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98697231.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56016
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.93
 p-value of test no 35                 :  9.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.91
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.63
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.57
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.46
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.98
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.22
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.96
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.16
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.04
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.28
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.57
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.73
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.09
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908460
   j =  2                              :            45764
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908506
   j =  2                              :            45744
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.14
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.33
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.74
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.81
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.96
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.83
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.73
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.71
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.71
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.14
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.50
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.02
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.18
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.74
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.06
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.27
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.96
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.47
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.41
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.03
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.93
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.02
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.53
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.91
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.72
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.25
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.45
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.16
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.17
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.09
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.45
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.39
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.46
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.07
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.61
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.13
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.85
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.17
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.22
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.84
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
 p-value of test no 213                :    0.9962
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9664.27
 p-value of test no 215                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.42
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.18
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.75
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.01
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.75
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.03
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.64
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000038155
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.44
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000055891
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9931
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:56.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99713039.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56017
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 11                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4184
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.06
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.40
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.74
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.71
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.61
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.18
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.50
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.77
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.63
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.35
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.55
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907762
   j =  2                              :            46113
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907981
   j =  2                              :            46005
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
 p-value of test no 80                 :    0.9961
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
 p-value of test no 91                 :    0.9978
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.40
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.94
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.58
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.49
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.42
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.36
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.07
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.44
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.41
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.68
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.54
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.48
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.57
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.79
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.03
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.31
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.08
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.71
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.33
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.49
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.14
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.03
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.05
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.27
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.59
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.20
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.12
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.82
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.40
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.38
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.85
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.70
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.24
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.30
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.94
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.22
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.90
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.08
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.32
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.46
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.96
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.84
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.32
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.94
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.30
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.31
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.22
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.82
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.25
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.14
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000081832
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.56
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999862016
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:34.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100728847.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56018
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4498
 p-value of test no 16                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    4.08
 p-value of test no 36                 :  8.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.45
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.38
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.96
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.43
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.32
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.86
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.31
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.07
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6915.21
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.17
 p-value of test no 61                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.14
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.03
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.27
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.13
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908476
   j =  2                              :            45759
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908069
   j =  2                              :            45958
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.98e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.22e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.49
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.83
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.12
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.12
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.42
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.71
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.27
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.72
 p-value of test no 136                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.14
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17475.17
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.69
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.84
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.55
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.93
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.95
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.10
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.23
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.93
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.50
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.46
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.43
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.63
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.72
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.62
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.71
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.31
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.58
 p-value of test no 165                :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.84
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.73
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.86
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.70
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.90
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.36
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.59
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.19
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.85
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.46
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.65
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   37.37
 p-value of test no 178                :  1.9e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 186                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 187                :  5.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 188                :  4.6e-3
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.27
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.28
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.24
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.14
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.64
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.78
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.22
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.55
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.72
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.96
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.12
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.85
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.33
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000025714
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.89
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000061603
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:44.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  81  LinearComp, r = 0               1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101777423.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56019
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 9                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 11                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.95
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.38
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.90
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.88
 p-value of test no 53                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  173.87
 p-value of test no 54                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.71
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.11
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.72
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.55
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.15
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.07
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.06
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.88
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908201
   j =  2                              :            45898
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46219
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907564
   j =  2                              :            46215
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 78                 :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.100
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.61
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.62
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.69
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.18
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.63
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.20
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.63
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.02
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.56
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17466.42
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.23
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.94
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.55
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.70
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.48
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.31
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.66
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.84
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.94
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.29
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.46
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.75
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.39
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.50
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.02
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.34
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.69
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.84
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.00
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.85
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.73
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.58
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.42
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.57
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.79
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.56
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.02
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.49
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.68
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.52
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.12
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 224                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4644.67
 p-value of test no 226                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.59
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.99
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11494.96
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.32
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.59
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000029419
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.86
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000016243
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9980
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.074
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:48.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102858767.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56020
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    4.69
 p-value of test no 39                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.60
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.18
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.99
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.82
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.21
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.33
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.41
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.43
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.77
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.57
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.08
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.01
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908120
   j =  2                              :            45937
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908445
   j =  2                              :            45773
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9908
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.32
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.78
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.07
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.67
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.38
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.31
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.72
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.39
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.34
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.83
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.41
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.85
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.37
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.04
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.65
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.83
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.93
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.46
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.64
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.41
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.86
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.14
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.90
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.57
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.71
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.72
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.36
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.45
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.22
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.21
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.60
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.97
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.24
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.24
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.32
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.84
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.76
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.82
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.13
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.12
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.78
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.49
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.31
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.61
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.04
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.58
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.84
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.88
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.00
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000037861
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.64
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999913484
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    2.39
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:11.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83296278.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56021
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    3.45
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.71
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.39
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.93
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.07
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.06
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.15
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.57
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.31
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7320.91
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.30
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.44
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.99
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.80
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907909
   j =  2                              :            46038
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908283
   j =  2                              :            45854
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.63e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.32
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.93
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.28
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.41
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.00
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.12
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.01
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.31
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.47
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.18
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17633.72
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.30
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.58
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.48
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.10
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.81
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.59
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.10
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.96
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.78
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.45
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.27
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.86
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.65
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.09
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.43
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.25
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.84
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.58
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.24
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.89
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.21
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.79
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.17
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.51
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.52
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.50
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.89
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.05
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.45
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.88
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.85
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.94
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.84
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.96
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.60
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.91
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.27
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.30
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.10
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.28
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999996950
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.85
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000004240
 
 Normal statistic for number of bits   :   0.034
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    2.41
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:43.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84377603.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56022
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    3.81
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.60
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.87
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.64
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.09
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.10
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.50
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.76
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.31
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.31
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1546.08
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.21
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.69
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.12
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.23
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5208.41
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907804
   j =  2                              :            46083
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907888
   j =  2                              :            46053
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
 p-value of test no 91                 :    0.9957
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -8.94e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.09
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.27
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.37
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.15
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.16
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.93
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.15
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.36
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.93
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17170.08
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.68
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.23
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.58
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.07
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.28
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.28
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.17
 p-value of test no 156                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.70
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.25
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.94
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.03
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.51
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.67
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.80
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.16
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.73
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.17
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.09
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.08
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.65
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.98
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.64
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.61
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.75
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.81
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.13
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.90
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.26
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.47
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.64
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.24
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.61
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.50
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.41
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.84
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.06
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.71
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.36
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000066994
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.88
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999941414
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.096
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:26.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85098499.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56023
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 6                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4524
 p-value of test no 17                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.43
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.84
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.63
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.34
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.47
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.96
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.60
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.13
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.61
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7211.29
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.58
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.08
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.76
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.45
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.73
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908570
   j =  2                              :            45709
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907863
   j =  2                              :            46061
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.36
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.22
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.54
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.27
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.13
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.70
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.41
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.42
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.85
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.40
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.88
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.40
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.96
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.27
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.61
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.53
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.88
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.92
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.37
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.34
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.22
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.29
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.72
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.78
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.94
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.82
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.23
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.98
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.14
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.55
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.70
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.09
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.92
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.74
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.00
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.48
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.07
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.85
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  292.01
 p-value of test no 174                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.43
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.52
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.55
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.37
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.81
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.44
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.11
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.93
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.00
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.59
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.39
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.43
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.96
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.94
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.21
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000052774
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.87
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000050761
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:51:40.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85950467.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56024
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 10                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1485
 p-value of test no 11                 :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     183
 p-value of test no 43                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    4.68
 p-value of test no 45                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.01
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.51
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.33
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.31
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.01
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.14
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  174.27
 p-value of test no 54                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.09
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.75
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.47
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.22
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.38
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.75
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.10
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.94
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908609
   j =  2                              :            45694
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46150
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907705
   j =  2                              :            46140
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.93
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.03
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.09
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.57
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.83
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.23
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.89
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.48
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.88
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.10
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.37
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.92
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.88
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.39
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.05
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.52
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.69
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.15
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.52
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.46
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.66
 p-value of test no 161                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.32
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.87
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.48
 p-value of test no 164                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.36
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.13
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.89
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.60
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.20
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.86
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.77
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.01
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.83
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.12
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.98
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.38
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.49
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.62
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.63
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9749.90
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.77
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.70
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.23
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.23
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.81
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.23
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   92.83
 p-value of test no 231                :  8.0e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999908555
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.38
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000070264
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 253                :  8.8e-3
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:47.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           6.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  101  Run of bits, r = 0              8.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87588867.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56025
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    4.08
 p-value of test no 27                 :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.07
 p-value of test no 29                 :  8.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.08
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.05
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.61
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.52
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.85
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.56
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.62
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.39
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.64
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.81
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.66
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.79
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.99
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907822
   j =  2                              :            46086
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907990
   j =  2                              :            45999
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  5.8e-3
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-5
 p-value of test no 110                :    0.9926
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.66
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.89
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.87
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.24
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.98
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.41
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.92
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.78
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.10
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.43
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17174.72
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.81
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.07
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.53
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.07
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.82
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.36
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.18
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.74
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.30
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.27
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.91
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.67
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.25
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.05
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.21
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.71
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.95
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.57
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.91
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.82
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.55
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.47
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.21
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.52
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.90
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.73
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.13
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.87
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.15
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.60
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.20
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.21
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.73
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.69
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.91
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.48
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.64
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.65
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.15
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000096982
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.40
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000036397
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:47.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88637443.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56026
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 11                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.75
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     549
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.39
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.09
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.44
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.77
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.48
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.99
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.11
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.24
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.34
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.89
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.42
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.44
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908325
   j =  2                              :            45830
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908766
   j =  2                              :            45611
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.20
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.85
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.18
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.25
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.12
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.49
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.15
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.04
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.53
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.91
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
 p-value of test no 138                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 139                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 140                :  3.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  184.86
 p-value of test no 141                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17235.21
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.65
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.23
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.20
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.37
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.77
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.54
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.25
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.27
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.26
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.79
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.22
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.46
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.90
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.80
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.03
 p-value of test no 164                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.18
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.35
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.56
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.84
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.46
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.16
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.64
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.81
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.28
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.12
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.78
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.78
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.44
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9976
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.70
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.88
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.04
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.68
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.07
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.52
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.71
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.94
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12075.74
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.71
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.11
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999855992
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.40
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000170362
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.057
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:47.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89653251.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56027
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.86
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.55
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   41.30
 p-value of test no 49                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.55
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.52
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.48
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.53
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.01
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.20
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.36
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.06
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.23
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.69
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.28
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.54
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.44
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908635
   j =  2                              :            45678
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908170
   j =  2                              :            45909
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.55
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.28
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.74
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.13
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.41
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.64
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.86
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.72
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.67
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.43
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.92
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.12
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.25
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.35
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.77
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.86
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.24
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.85
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.54
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.23
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.23
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.81
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.29
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.43
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.78
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.68
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.77
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.79
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.84
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.47
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.61
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.39
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.70
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.89
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.98
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.08
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.50
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.82
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.52
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.10
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.42
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.20
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.78
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.02
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.94
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.71
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.73
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.86
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.25
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.13
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.19
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.64
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000084868
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.94
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000139651
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.54e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:23.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90669059.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56028
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 28                 :    0.9974
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 33                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.36
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.82
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.65
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.67
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.21
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.97
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.91
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.30
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.34
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.53
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.95
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.37
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907892
   j =  2                              :            46054
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45484
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869484
   j =  1                              :        399909036
   j =  2                              :            45476
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.67
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.70
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.50
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.73
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.74
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.46
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.31
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.37
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.21
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.01
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17148.41
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.39
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.67
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.05
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.46
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.82
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.29
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.40
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.16
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.04
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.29
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.31
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.81
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.67
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.59
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.46
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.03
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.42
 p-value of test no 165                :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.43
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.74
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.80
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.97
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.20
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.13
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.23
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.97
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.79
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.88
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.64
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.22
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 182                :  1.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.11
 p-value of test no 183                :    0.9991    *****
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.02
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.94
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.40
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.32
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.96
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.46
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.11
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.49
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.44
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11623.47
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.88
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.98
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999947810
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   88.53
 p-value of test no 233                :  2.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999964727
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    2.21
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:03.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  82  LempelZiv, r = 0                0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91684867.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56029
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7069
 p-value of test no 20                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.86
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.84
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.69
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.28
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.59
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.45
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.88
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.10
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.53
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.92
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.63
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.74
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.29
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.32
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907735
   j =  2                              :            46128
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908302
   j =  2                              :            45843
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 86                 :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 88                 :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.50
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.64
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.05
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.71
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.28
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.25
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.89
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.61
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.56
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.83
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.49
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.73
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.85
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.24
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.12
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.21
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.81
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.48
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.34
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.03
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.91
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.74
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.98
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.19
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.30
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.32
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.99
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.61
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.50
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.91
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.74
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.40
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.21
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.13
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.57
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.76
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.21
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.26
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.14
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.65
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.67
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.04
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.73
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.53
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.80
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.19
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.41
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3898.24
 p-value of test no 228                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.23
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.00
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.95
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000000439
 
 Normal statistic for number of bits   : 3.47e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.09
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000056125
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:29.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92635139.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56030
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 11                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4494
 p-value of test no 16                 :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4199
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.09
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.30
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.73
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.22
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.83
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.49
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.71
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.71
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.32
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.58
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.32
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.99
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.62
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908192
   j =  2                              :            45898
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908714
   j =  2                              :            45637
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -7.85e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 117                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.36
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.05
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.22
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.21
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.83
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.03
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.27
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.27
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.85
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.63
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.85
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.32
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.42
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.70
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.87
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.37
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.12
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.44
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.74
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.20
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.34
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.01
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.78
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.14
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.53
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.99
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.49
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.61
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.66
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.68
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.42
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.50
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  302.30
 p-value of test no 171                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.23
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.48
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.19
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.83
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.79
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.26
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.97
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.23
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.58
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.45
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.45
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.86
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.48
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.80
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.97
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.39
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.73
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.73
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999837206
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.59
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999923672
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.079
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:11.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 H (L=10000, r=15)   0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93585411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56031
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7102
 p-value of test no 15                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.63
 p-value of test no 48                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.63
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.27
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.97
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.66
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.42
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.09
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.58
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.16
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.14
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.38
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.97
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.72
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.61
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907996
   j =  2                              :            45996
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46299
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870299
   j =  1                              :        399907408
   j =  2                              :            46287
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.19
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.80
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.86
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.66
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.87
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.34
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.54
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.28
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17259.79
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.97
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.33
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.13
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.91
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.30
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.92
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.63
 p-value of test no 155                :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.11
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.58
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.36
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.22
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.26
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.75
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.97
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.25
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.24
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.70
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.89
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.93
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.55
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.36
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.61
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.50
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.50
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.45
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.43
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.61
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    2.02
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.99
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.35
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.51
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.05
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.98
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.41
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.34
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.74
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.69
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.15
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.46
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000157189
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.85
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000039586
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94568451.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56032
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.55
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.62
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.02
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.05
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.72
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.60
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.99
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1305.84
 p-value of test no 56                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.36
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.35
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.54
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.50
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.66
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908330
   j =  2                              :            45832
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908373
   j =  2                              :            45809
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.95
 p-value of test no 115                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.51
 p-value of test no 117                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.12
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.99
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.81
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.48
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.70
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.46
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.64
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.91
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.97
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.90
 p-value of test no 134                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.99
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.45
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.31
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17702.00
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.57
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.19
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.20
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.13
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.55
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.26
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.87
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.43
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.19
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.99
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.49
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.35
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.42
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.49
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.84
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.63
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.62
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.54
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.66
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.36
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.76
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.45
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.89
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.21
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.35
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.31
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.81
 p-value of test no 172                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.84
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.62
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.79
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.12
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.25
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.30
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.47
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.69
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.53
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.66
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.65
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.14
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.91
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.16
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.58
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000127702
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.40
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999953855
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:26.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95453187.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56033
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.90
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.45
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.42
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.43
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.14
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.90
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.92
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.36
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.87
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1548.50
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.67
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.76
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.57
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.88
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.58
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.27
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907741
   j =  2                              :            46125
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908236
   j =  2                              :            45876
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.77
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.61
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.01
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.02
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.57
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.78
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.19
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
 p-value of test no 138                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.05
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.31
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.67
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.20
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.30
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.65
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.12
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.99
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.98
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.37
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.75
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.98
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.24
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.58
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.15
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.55
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.95
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.71
 p-value of test no 161                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.22
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.36
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.05
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.03
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.04
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.95
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.65
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.70
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.95
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.94
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.04
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.72
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.51
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.78
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.75
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.13
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.65
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.45
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.11
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.73
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.04
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.68
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.85
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.78
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.24
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.88
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.71
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.56
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000002620
 
 Normal statistic for number of bits   :   0.021
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.16
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999815291
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:45.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96600067.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56034
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997249
   j =  2                              :             1374
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.09
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.87
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.74
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.86
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.49
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.38
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.12
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.42
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.39
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.28
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.39
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908343
   j =  2                              :            45824
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 84                 :  4.1e-5    *****
 
 Anderson-Darling statistic = A2       :    5.98
 p-value of test no 85                 :  1.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.72e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.07
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.74
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.43
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.07
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.73
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.41
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.61
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.39
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.61
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.98
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.62
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.24
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.35
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.05
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.91
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.88
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.39
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.71
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.30
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.81
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.91
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.25
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.24
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.61
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.61
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.92
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.44
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.89
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.26
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.77
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.80
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.41
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.05
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.08
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.53
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.33
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.68
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.22
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.50
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.98
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.69
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.19
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9714.91
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.65
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.00
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.58
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.64
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.94
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.44
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.04
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999957383
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.47
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999988661
 
 Normal statistic for number of bits   :  -0.090
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:22.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97583107.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56035
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.94
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.23
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.67
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.39
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.22
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.95
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  183.77
 p-value of test no 54                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.44
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.48
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.72
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.02
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.31
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.20
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.64
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908069
   j =  2                              :            45961
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908135
   j =  2                              :            45931
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.42
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.85
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.92
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.37
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.45
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.56
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.76
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.60
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.52
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.72
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.99
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.05
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.20
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.01
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.13
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.45
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.77
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.97
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.32
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.32
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.84
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.11
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.95
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.34
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.49
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.88
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.28
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.56
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.04
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.74
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.23
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.23
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.75
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.23
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.80
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.69
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.10
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.04
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.54
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.48
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.56
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.25
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.15
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.11
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.35
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.61
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.33
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.02
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.62
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.89
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.11
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999926618
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.72
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000128188
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:32.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98566147.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56036
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.02
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.78
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.98
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.86
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.60
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.70
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.58
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.70
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.02
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.13
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6872.75
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.96
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.78
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.29
 p-value of test no 66                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.82
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5217.57
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908227
   j =  2                              :            45885
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908366
   j =  2                              :            45811
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 79                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 81                 :  1.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9990    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.13
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.55
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.58
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.34
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.04
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.63
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.02
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.45
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.29
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17454.14
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.85
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.08
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.53
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.09
 p-value of test no 149                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.35
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.66
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.23
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.22
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.96
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.06
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.29
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   91.87
 p-value of test no 159                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.17
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.55
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.32
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.84
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.64
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.39
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.55
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.71
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.65
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.28
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.89
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.19
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.50
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.60
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.01
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.34
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.02
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.38
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.00
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.54
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.34
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.40
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.04
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.45
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.25
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.82
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12165.91
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12132.83
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.70
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999932285
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.12
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000020518
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:05.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9990 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99581955.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56037
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.10
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.36
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.42
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.15
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.90
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.55
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.49
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.51
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.34
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.09
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.01
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.64
 p-value of test no 59                 :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.59
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.07
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.70
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.56
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907836
   j =  2                              :            46076
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908017
   j =  2                              :            45984
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 100                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.77
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.29
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.44
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.77
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.49
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   55.10
 p-value of test no 125                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.70
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.42
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.23
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.24
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.73
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.89
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.56
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.48
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.54
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.78
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.86
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.71
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.30
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.50
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.27
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.03
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.93
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.00
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.34
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.00
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.80
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.63
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.37
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.80
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.06
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.42
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.20
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.95
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.57
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5296.88
 p-value of test no 173                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.59
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.62
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.99
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.85
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.41
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.63
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.60
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.35
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.13
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.23
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.47
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4342.13
 p-value of test no 228                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.50
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.43
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.99
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000070741
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.27
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999847835
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:56.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100532227.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56038
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7602
 p-value of test no 15                 :  5.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.13
 p-value of test no 23                 :  7.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.75
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.22
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.66
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.32
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.62
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.48
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.81
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.63
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.74
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.40
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.84
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.43
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.62
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5146.22
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908356
   j =  2                              :            45819
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907921
   j =  2                              :            46035
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.071
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.25
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.41
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.79
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.47
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.59
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.78
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.04
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.31
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.43
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.59
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.91
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.34
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.15
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.66
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.17
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.15
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.38
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.58
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.59
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.49
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.69
 p-value of test no 161                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.43
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.38
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   89.58
 p-value of test no 164                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.73
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.89
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.77
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.17
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.31
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.91
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.35
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.69
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.30
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.59
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.12
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.36
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.63
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.68
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.31
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.59
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.69
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.02
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.72
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.86
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.66
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.43
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.76
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12224.20
 p-value of test no 230                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.45
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999933497
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.15
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999922007
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.91
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:03.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         5.0e-4
  77  RandomWalk1 R (L=1000, r=20)    0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101548035.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56039
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 6                  :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.26
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.05
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.63
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.30
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.30
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.92
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.32
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.87
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.92
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.74
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.89
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.64
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.64
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.68
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.79
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.08
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908071
   j =  2                              :            45960
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908002
   j =  2                              :            45993
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.94
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.41
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.60
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.10
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.88
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.68
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.78
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.33
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.78
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.94
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.45
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.35
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.93
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.44
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.90
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.49
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.07
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.80
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.94
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.11
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.17
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.11
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.77
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.27
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.43
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.37
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.92
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.65
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.17
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.07
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.53
 p-value of test no 171                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.91
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.75
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.77
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.84
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.21
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.07
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9702.13
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.35
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.27
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.64
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.70
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.68
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.09
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.87
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.13
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999908378
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.44
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000051328
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    2.23
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 251                :  1.0e-2
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 253                :  8.9e-3
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:08.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102563843.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56040
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7516
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    4.23
 p-value of test no 33                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.00
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.04
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.16
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.86
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.52
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.03
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.22
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.67
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.82
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.10
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.46
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.07
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.81
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.63
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908517
   j =  2                              :            45740
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908139
   j =  2                              :            45923
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.04
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.13
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.62
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.43
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.44
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.07
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.33
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.83
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.72
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 139                :    0.9903
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   98.54
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.16
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.88
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.51
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.62
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.93
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.36
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.53
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.88
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.08
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.07
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.75
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.67
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.32
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.26
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.22
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.63
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.12
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.58
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.34
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.69
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.57
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.43
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.02
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.01
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.15
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.69
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.05
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.47
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.93
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.77
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.62
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.02
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.14
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.43
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.89
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.96
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.50
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.15
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.44
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11456.37
 p-value of test no 230                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.91
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999855965
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.43
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999932570
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :   0.079
 p-value of test no 239                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:03.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83329047.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56041
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.54
 p-value of test no 35                 :  1.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.44
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.74
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.07
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.53
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.35
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.41
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.98
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.37
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.89
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.17
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.93
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.03
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.50
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.45
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908303
   j =  2                              :            45844
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.40
 p-value of test no 117                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.07
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.81
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.97
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.65
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.27
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.10
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.79
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.29
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.73
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.32
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17821.96
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.39
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.17
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.44
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.80
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.54
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.58
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.28
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.33
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.08
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.63
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.34
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.03
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.47
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.33
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.93
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.43
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.65
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.73
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  455.63
 p-value of test no 169                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.65
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.06
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.93
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.54
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.01
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.23
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    2.23
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.67
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.20
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.55
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.04
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.87e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.57
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.75
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.88
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.05
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.44
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.72
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.94
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999935927
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.86
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000045217
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -2.46e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:58.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84344855.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56042
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.10
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.30
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.44
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.18
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.46
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.91
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.47
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.86
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.08
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.86
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.46
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.64
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.23
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907845
   j =  2                              :            46073
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.75
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.17
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.71
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.57
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.07
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.97
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.63
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.25
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.30
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.30
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.55
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.48
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.95
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.73
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.16
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.57
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.36
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.61
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.99
 p-value of test no 157                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.06
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.43
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.05
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.54
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.35
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.15
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.66
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.43
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.90
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.79
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.74
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.84
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.69
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.79
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.26
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.72
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.70
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.14
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.10
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.93
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.45
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.53
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.19
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.00
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.52
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.81
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.28
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5099.72
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.24
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4301.99
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.29
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.01
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.66
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999942335
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.12
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000094162
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:28.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85393431.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56043
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.74
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.89
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.04
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.09
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.24
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.90
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.41
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.74
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.67
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.82
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.75
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.96
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908388
   j =  2                              :            45800
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908030
   j =  2                              :            45976
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 77                 :    0.9954
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.05
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.02
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.08
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.57
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.38
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.15
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.90
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.63
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.03
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.13
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17828.68
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.63
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.16
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.57
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.47
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.64
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.48
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.93
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.79
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.22
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.02
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.83
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.47
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.27
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.96
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.02
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.64
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.81
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.25
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.67
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.66
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.73
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.33
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.52
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.72
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.72
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.85
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.99
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.68
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.21
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.18
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.66
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.11
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.13
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.18
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.70
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.01
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.80
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.08
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.91
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.14
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.08
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.25
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000093328
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.15
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999956195
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:33.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86409239.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56044
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 3                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 4                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7614
 p-value of test no 15                 :  3.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7103
 p-value of test no 20                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.46
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.54
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.76
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.66
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.02
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.88
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.71
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.84
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.13
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.64
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.02
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.16
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.66
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.07
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45449
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869449
   j =  1                              :        399909107
   j =  2                              :            45439
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46501
 p-value of test no 71                 :  1.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870501
   j =  1                              :        399907001
   j =  2                              :            46495
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 93                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.03
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.59
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.89
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.76
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.96
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.06
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.65
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.80
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.64
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.76
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.36
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.47
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.06
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.23
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.43
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.65
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.02
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.60
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.65
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.91
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.17
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.66
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  205.94
 p-value of test no 162                :  8.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.21
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.03
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.38
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.38
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.21
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.83
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.83
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.42
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.95
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.16
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.96
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.44
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.54
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.32
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.25
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.04
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.75
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.03
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.19
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 216                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.11
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
 p-value of test no 224                :    0.9964
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.98
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.71
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.88
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.76
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.85
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.09
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999852596
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000057691
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:32.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         3.0e-4
  77  RandomWalk1 M (L=1000, r=20)    8.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87425047.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56045
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.77
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.10
 p-value of test no 47                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.57
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.04
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.61
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.07
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.29
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.02
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.28
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.35
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.36
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.67
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.85
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.84
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.08
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908290
   j =  2                              :            45849
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908561
   j =  2                              :            45706
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.69
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.92
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.95
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.12
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.93
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.55
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.14
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.13
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.29
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.87
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.85
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.38
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.13
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.96
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.88
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.06
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.60
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.50
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.94
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.21
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.47
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.86
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.27
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.31
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.31
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.68
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.86
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.11
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.91
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.18
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.57
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.94
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.35
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.09
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.05
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.46
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.29
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.84
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.15
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.63
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.30
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.99
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.75
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.12
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.23
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.35
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.61
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.27
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.37
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.64
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000051667
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000033742
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:37.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88408079.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56046
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5277
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.63
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.30
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.72
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.69
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.90
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.28
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.19
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.31
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.53
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.73
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.61
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.48
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.57
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.14
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4926.24
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908001
   j =  2                              :            45998
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907759
   j =  2                              :            46113
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.66
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.92
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.95
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.42
 p-value of test no 122                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.64
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.24
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.39
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.72
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.14
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.07
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.92
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.01
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.35
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.75
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.01
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.34
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.16
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.43
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.21
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.45
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.12
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.24
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.03
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.63
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.56
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.67
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.66
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.68
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.25
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.61
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.82
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.51
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.82
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.92
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.28
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.98
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.10
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.11
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.26
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.16
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.61
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.42
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.92
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.42
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.28
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.15
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.10
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.74
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000051820
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.33
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999966368
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9918
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:29.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89227279.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56047
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.95
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.12
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.55
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.23
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.76
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.82
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.39
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.45
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.48
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.23
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.32
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.06
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.13
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.14
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.16
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908383
   j =  2                              :            45807
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908314
   j =  2                              :            45840
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.81
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.02
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.14
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.11
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.01
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.59
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.35
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.34
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.91
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.15
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17203.25
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.36
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.70
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.63
 p-value of test no 150                :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.85
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.36
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.24
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.99
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.02
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.97
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.17
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.29
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.73
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.22
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.34
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.24
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.31
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.33
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.50
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.24
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.42
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.33
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.71
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.19
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.72
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.39
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.53
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.91
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.47
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.84
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.90
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.03
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.58
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.64
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.03
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.97
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.54
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.63
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.74
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.18
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.17
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000083935
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.81
 p-value of test no 233                :  5.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999846878
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:44.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90374159.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56048
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 11                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.9907
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    3.54
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.39
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.44
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.34
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.02
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.63
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.02
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.36
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.83
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.31
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.96
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.27
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.00
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.10
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45441
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869441
   j =  1                              :        399909123
   j =  2                              :            45431
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908222
   j =  2                              :            45886
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.56
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.64
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.54
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.74
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.33
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.25
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.26
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.57
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.21
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.20
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.35
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.31
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.61
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.25
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.08
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.93
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.94
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.81
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.22
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.24
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.69
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.37
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.67
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.07
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.32
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.30
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.60
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.19
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.59
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.92
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  253.93
 p-value of test no 170                :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.05
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.28
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.36
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.70
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.44
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.84
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.52
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.95
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.29
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.12
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.82
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.69
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4327.45
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.87
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.61
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.01
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.55
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999970910
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.97
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000152989
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    2.35
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:07.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91422735.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56049
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 4                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997337
   j =  2                              :             1330
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    4.72
 p-value of test no 24                 :  3.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9938
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9943
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.33
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.45
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.35
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.44
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.86
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.29
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.60
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.39
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.85
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.22
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.96
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.31
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.66
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.46
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.24
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.33
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907981
   j =  2                              :            46002
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45650
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869650
   j =  1                              :        399908705
   j =  2                              :            45640
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.85
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.40
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.83
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.81
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.80
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.63
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.63
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.06
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.86
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17342.97
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.11
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.96
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.07
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.56
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.48
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.39
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.31
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.53
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.91
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.31
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.68
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.05
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.99
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.96
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.16
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.10
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.73
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.21
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.04
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.25
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.71
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.02
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.39
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.53
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.01
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.33
 p-value of test no 175                :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.21
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.35
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.24
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.13
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.17
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9789.50
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.36
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.15
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.16
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.47
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.52
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.69
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.21
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999865478
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.69
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999911876
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:40.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92405775.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56050
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.87
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.05
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.97
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.65
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.32
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.73
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.95
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.85
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.23
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.51
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.82
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.21
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.41
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908532
   j =  2                              :            45728
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908088
   j =  2                              :            45947
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.88
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.26
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.34
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.69
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.26
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.60
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.60
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.47
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.80
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.90
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.06
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.23
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.67
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.73
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.37
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.61
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.56
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.02
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.25
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.44
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.72
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.87
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.57
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.72
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.37
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.33
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.60
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.66
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.58
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.33
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.08
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.55
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.53
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.98
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.78
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.31
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.25
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.81
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.68
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.71
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.55
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.59
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.58
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.22
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.32
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.63
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.84
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.74
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.55
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.29
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.66
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.15
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000113047
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.69
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999886010
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:16.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93323284.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56051
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4201
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.85
 p-value of test no 46                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.10
 p-value of test no 47                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.71
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.86
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.28
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.93
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.05
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.09
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.23
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.66
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.69
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.68
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.89
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907759
   j =  2                              :            46110
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907961
   j =  2                              :            46015
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.52
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.02
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.10
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.77
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.32
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.86
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.43
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.03
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.67
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.85
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.57
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.43
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.08
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.46
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.15
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.42
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.07
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.63
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.42
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.10
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.25
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.32
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.38
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.39
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.83
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.40
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.59
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.42
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.70
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.89
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.01
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.94
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.26
 p-value of test no 172                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.72
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.11
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.80
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.55
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.30
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.30
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.13
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.08
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.51
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5133.69
 p-value of test no 222                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.62
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.41
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.93
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11575.90
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.66
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.56
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000007846
 
 Normal statistic for number of bits   :   0.062
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.95
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000015451
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:23.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94175252.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56052
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 5                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5590
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.11
 p-value of test no 29                 :  7.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.23
 p-value of test no 34                 :  7.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 39                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.08
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.34
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.10
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.61
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.65
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.20
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.07
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.47
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  510.91
 p-value of test no 55                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.50
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6851.55
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.53
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.57
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.29
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.11
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.96
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45443
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869443
   j =  1                              :        399909118
   j =  2                              :            45435
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907899
   j =  2                              :            46046
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
 p-value of test no 100                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.6e-3
 
 Anderson-Darling statistic = A2       :    7.20
 p-value of test no 102                :  2.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.83
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.78
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.65
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.11
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.77
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.10
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.34
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.36
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.89
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.50
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.96
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.79
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.97
 p-value of test no 157                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.30
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.25
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.53
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.23
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.44
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.32
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.47
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.96
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.57
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.08
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.27
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.93
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.94
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.82
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.56
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.55
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.71
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.59
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.04
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.03
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.12
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.66
 p-value of test no 216                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.72
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.43
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.77
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.68
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.66
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.96
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.46
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000197728
 
 Normal statistic for number of bits   :    1.56
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.01
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000048409
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:37.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               2.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95191060.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56053
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997352
   j =  2                              :             1321
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.80
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.89
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.70
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.98
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.15
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.63
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.46
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6873.95
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.40
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.03
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.87
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  157.05
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.92
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908228
   j =  2                              :            45880
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908339
   j =  2                              :            45823
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.58
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.91
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.04
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.97
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.50
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.76
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.19
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.73
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.68
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.65
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.35
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.55
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.29
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.43
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.47
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.03
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.60
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.09
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.48
 p-value of test no 155                :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.46
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.95
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.64
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.06
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.19
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.40
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.99
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.75
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.45
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.97
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.73
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.43
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  476.91
 p-value of test no 169                :  4.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.23
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.66
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.33
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.00
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.53
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.05
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.07
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.81
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.69
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.62
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 208                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 209                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10374.41
 p-value of test no 211                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.53
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.94
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.46
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.89
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.44
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.33
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.62
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.09
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999883946
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.10
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000097978
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    2.18
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:22.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 R (L=10000, r=0)    4.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96567316.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56054
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 7                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.27
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.55
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.09
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.55
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.57
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.32
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.27
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.97
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.37
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.23
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.73
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 64                 :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.77
 p-value of test no 65                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.80
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.80
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.21
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908219
   j =  2                              :            45886
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908376
   j =  2                              :            45806
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9904
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.19
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.19
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.98
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.13
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.22
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.27
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.52
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 130                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 131                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    6.81
 p-value of test no 132                :  4.5e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   80.85
 p-value of test no 133                :  1.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.92
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17102.74
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.44
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.71
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.61
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.37
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.80
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.95
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.02
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.81
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.87
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.62
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.46
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.56
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.05
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.24
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.15
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.00
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.34
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.08
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.01
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.21
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.48
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.02
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.71
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.50
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.76
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.04
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.84
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.26
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.12
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.70
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.45
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 181                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.46
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.86
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.77
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.97
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.04
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.49
 p-value of test no 216                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.78
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.86
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.96
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.47
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.06
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.96
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.17
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999887804
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.28
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999812081
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:03.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          1.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97517588.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56055
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1499
 p-value of test no 5                  :  1.7e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334619
   j =  1                              :        599997002
   j =  2                              :             1499
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 7                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.24
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.49
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.78
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.78
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.65
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.88
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.65
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.01
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.15
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.04
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.99
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.73
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.54
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4857.78
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907764
   j =  2                              :            46115
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908543
   j =  2                              :            45718
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.14
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.02
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.35
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.63
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.93
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.94
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.60
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.21
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.38
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.17
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.08
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.35
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.42
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.74
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.89
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.79
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.43
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.22
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.07
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.04
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.80
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.11
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.84
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.22
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.30
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.53
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.63
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.36
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.57
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.85
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.63
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.70
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.18
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.64
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5285.53
 p-value of test no 173                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.23
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.40
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.41
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.88
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.05
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.70
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.72
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.45
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.39
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.45
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.88
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.82
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.35
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.43
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000187570
 
 Normal statistic for number of bits   :    1.48
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.15
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999999449
 
 Normal statistic for number of bits   : -4.36e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:13.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            1.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98598932.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56056
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.29
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.45
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.15
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.56
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.56
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.76
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.02
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.40
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.02
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.31
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5221.79
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908604
   j =  2                              :            45692
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46260
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870260
   j =  1                              :        399907483
   j =  2                              :            46254
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.69e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.39
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.15
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.17
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.99
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.97
 p-value of test no 125                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 126                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.49
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.79
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.32
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.17
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17592.81
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.92
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.85
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.65
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.94
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.42
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.02
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.29
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.14
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.80
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.20
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.24
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.99
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.10
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.01
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.04
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.36
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.03
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.70
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.49
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.54
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.21
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.65
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.54
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.64
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.56
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.77
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.41
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.85
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.14
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.71
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.64
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.07
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.69
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.12
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.93
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.95
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.92
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.57
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.70
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000077914
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999984917
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.056
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99516436.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56057
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 17                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.60
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.51
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.34
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.01
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.20
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.95
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.82
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.26
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.71
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.08
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.54
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.15
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.17
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.12
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.78
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908699
   j =  2                              :            45649
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908740
   j =  2                              :            45624
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 117                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.52
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.33
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.16
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.00
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.29
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.69
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.95
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.96
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.88
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.82
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.06
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.42
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.05
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.44
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.41
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.84
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.50
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.87
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.37
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.68
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.52
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.05
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  577.49
 p-value of test no 158                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.16
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.31
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.81
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.85
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.66
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.15
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.99
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.62
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.98
 p-value of test no 167                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.59
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.92
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.66
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.37
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.65
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.50
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.23
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.62
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.38
 p-value of test no 178                :  6.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.38
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.21
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.68
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.48
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.64
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.63
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.36
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.86
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.15
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.81
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.60
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.17
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.54
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000004951
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.09
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999962996
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.041
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:56.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100663316.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56058
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    3.64
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.35
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.16
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.34
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.93
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.22
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.24
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.02
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1586.16
 p-value of test no 56                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.95
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.24
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.37
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.78
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.95
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908090
   j =  2                              :            45949
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46223
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870223
   j =  1                              :        399907557
   j =  2                              :            46217
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 72                 :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-4
 p-value of test no 109                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.81
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.81
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.07
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.42
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.86
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.09
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.77
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.16
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.02
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.42
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.44
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.67
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.50
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.25
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.68
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.48
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.34
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.48
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.14
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.03
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.96
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.79
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.50
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.15
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.97
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.87
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.05
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.73
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.98
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.25
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.70
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.71
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.14
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.84
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.53
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.27
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.42
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.24
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.06
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.90
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.99
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.18
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9821.95
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.53
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.48
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.09
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.51
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.11
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.28
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.19
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.02
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000050368
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.43
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000184654
 
 Normal statistic for number of bits   :    1.46
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:18.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101613588.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56059
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.61
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.18
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.42
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.69
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.57
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.15
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.87
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.53
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.06
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.08
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.33
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.77
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.26
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907850
   j =  2                              :            46072
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908308
   j =  2                              :            45840
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.65
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.56
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.25
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.09
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.21
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.79
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.07
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.60
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.66
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.56
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.67
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.55
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.86
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.51
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.84
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.85
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.39
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.18
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.07
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.70
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.96
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.65
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.81
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.68
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.09
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.77
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.49
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.30
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.11
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.03
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.80
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.67
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.32
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.09
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.32
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.96
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.76
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.15
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.75
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.45
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.40
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.75
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.90
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.64
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.97
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.27
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.19
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.71
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.73
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.34
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12172.59
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.06
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000010243
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.23
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000183124
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 245                :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    5.39
 p-value of test no 247                :  2.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.14
 p-value of test no 248                :  8.3e-4    *****
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:45.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  105  AutoCor, d=1, r=27              8.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102662164.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56060
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.74
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.89
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.88
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.92
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.31
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.48
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.86
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.68
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.93
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.77
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.09
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.16
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.26
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4905.64
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908729
   j =  2                              :            45631
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45656
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869656
   j =  1                              :        399908694
   j =  2                              :            45644
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-4
 p-value of test no 109                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.94
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.45
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.84
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.88
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.16
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.05
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.64
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.75
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.90
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.42
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   67.20
 p-value of test no 146                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.65
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.16
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.73
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.49
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.41
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.00
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.19
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.04
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.11
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.48
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.04
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.08
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.31
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.25
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.40
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.76
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.99
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.86
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.43
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.22
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.09
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.15
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.95
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.73
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.81
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.95
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.53
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.32
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.24
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.72
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.82
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.68
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.79
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.59
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.05
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.22
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.08
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000147895
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.94
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000143503
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.42e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:38.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83361816.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56061
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5245
 p-value of test no 13                 :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 35                 :    0.9988
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.67
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.30
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.38
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.84
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.88
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   92.17
 p-value of test no 51                 :  9.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.88
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.87
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.65
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.93
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.05
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.41
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.69
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.41
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.19
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46183
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907638
   j =  2                              :            46175
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908018
   j =  2                              :            45985
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9900
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.98
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.51
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.95
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.92
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.03
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.08
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.67
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.48
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.20
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.64
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.09
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.19
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.43
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.02
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.72
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.97
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.71
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.95
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.97
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.70
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.50
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.01
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.75
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.57
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.01
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.23
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.77
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.20
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.88
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.70
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.74
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.79
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.92
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.19
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.23
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.83
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.37
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.07
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.30
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.76
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.44
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.10
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.18
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.52
 p-value of test no 196                :    0.9924
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.79
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.42
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.64
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.91
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.17
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.87
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.64
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.22
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.12
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.28
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.65
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000133564
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.16
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000062389
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:24.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         9.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83886090.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56062
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.45
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.43
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.33
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.94
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.35
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.01
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.93
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.75
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.54
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.69
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.66
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.28
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.05
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.79
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908344
   j =  2                              :            45822
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907604
   j =  2                              :            46192
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.76
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.51
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.26
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.56
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.03
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.66
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.04
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.74
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.91
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.50
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.23
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.39
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.72
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.83
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.42
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.28
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.15
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.52
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.71
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.98
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.72
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.60
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  604.06
 p-value of test no 158                :  9.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.97
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.77
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.56
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.71
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.46
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.45
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.65
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.10
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.59
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.65
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.48
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.24
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.71
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.66
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4757.67
 p-value of test no 173                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.32
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.51
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.23
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    2.57
 p-value of test no 189                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.60
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.14
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.94
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.08
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.70
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.27
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.39
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.16
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.83
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.91
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.45
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.24
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999936797
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.57
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000018070
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
 p-value of test no 236                :    0.9956
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 237                :  6.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.91
 p-value of test no 238                :    0.9982
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:38.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 J (L=1000, r=0)     9.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84770826.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56063
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 11                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.93
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.83
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.08
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.03
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.50
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.69
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.07
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.18
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.10
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.23
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.81
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.12
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5263.72
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908440
   j =  2                              :            45771
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46161
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870161
   j =  1                              :        399907682
   j =  2                              :            46153
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-5
 p-value of test no 113                :    0.9955
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.16
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.04
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.11
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.13
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.62
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.55
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.74
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.59
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.45
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17070.66
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.89
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.64
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.34
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.97
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.86
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.88
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.43
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.00
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.15
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.43
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.67
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.10
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.06
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.33
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.31
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.98
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.12
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.41
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.24
 p-value of test no 166                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.07
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.25
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.07
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.61
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.50
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.66
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.31
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.03
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.15
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.03
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.23
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.71
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.34
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9788.90
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.92
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 217                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.84
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.96
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.72
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.28
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.57
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12109.80
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.98
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999928919
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.80
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000123400
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85655562.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56064
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.34
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.46
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.34
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.47
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.77
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.52
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.82
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.38
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.90
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.43
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.64
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.13
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907564
   j =  2                              :            46212
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46303
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870303
   j =  1                              :        399907396
   j =  2                              :            46299
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.02
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.26
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.24
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.80
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.62
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.42
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.03
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.15
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.18
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.02
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.44
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.72
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.15
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.52
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.09
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.11
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.15
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.46
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.68
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.07
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.13
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.44
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.80
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.68
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.76
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.79
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.82
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.81
 p-value of test no 166                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.46
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.45
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.22
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.75
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.84
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.90
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.20
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.24
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.08
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.33
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.50
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.49
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.72
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.71
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.28
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.08
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4686.85
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.50
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.31
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.21
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.37
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.13
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999965915
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.07
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999867203
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:21.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86671370.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56065
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.98
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.50
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.62
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.21
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.65
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.19
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.85
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.33
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.55
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.30
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.85
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.15
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.46
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.68
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.42
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908340
   j =  2                              :            45824
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908300
   j =  2                              :            45844
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 106                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.13
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.96
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.23
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.13
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.04
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.13
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.42
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.91
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.84
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.77
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.07
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.74
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.21
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.82
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.74
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.05
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.61
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.48
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.66
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.19
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.96
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.53
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.50
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.67
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.17
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.33
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.83
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.06
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.21
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.66
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.38
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.51
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.68
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.51
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.25
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.39
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.43
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.91
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.04
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.34
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.34
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.39
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.20
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.40
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.44
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.06
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.97
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.37
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.79
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11592.99
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.81
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000109858
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.91
 p-value of test no 233                :  3.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000046267
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.023
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    2.38
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.46e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:47.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87719946.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56066
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.70
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.40
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.66
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.30
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.81
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.20
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.30
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.69
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.07
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.50
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.79
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.76
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.02
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.58
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5218.30
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908596
   j =  2                              :            45693
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907883
   j =  2                              :            46054
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.64
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.00
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.73
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.80
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.11
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.57
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   15.22
 p-value of test no 136                :  4.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.76
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17209.71
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.53
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.82
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.22
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.38
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.55
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.70
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.20
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.91
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.15
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.94
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.21
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.14
 p-value of test no 160                :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.54
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.96
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.31
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.13
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.27
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.21
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.18
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.68
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.02
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.98
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.89
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.36
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.24
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.87
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.58
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.18
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.20
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.94
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.26
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.60
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.13
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.83
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.57
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.35
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.01
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.29
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.08
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.07
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.78
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000054973
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.97
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999977033
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:19.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              4.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88735754.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56067
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1487
 p-value of test no 11                 :  5.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334607
   j =  1                              :        599997026
   j =  2                              :             1487
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.98
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.56
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.85
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.07
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.07
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.34
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.34
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.24
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.91
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.90
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.16
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.20
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.38
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.08
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907996
   j =  2                              :            45996
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908225
   j =  2                              :            45883
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 77                 :    0.9943
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-7
 p-value of test no 113                : 1 -  2.4e-5    *****
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.53
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.48
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.16
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.93
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.79
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.42
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.40
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.39
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.84
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.18
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.35
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   52.07
 p-value of test no 148                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.48
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.09
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.37
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.91
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.08
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.62
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.76
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  417.69
 p-value of test no 158                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.83
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.66
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.85
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.67
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.41
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.34
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.80
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.18
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.12
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.88
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.50
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.89
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.42
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.22
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.70
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.41
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.30
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.06
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.73
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.70
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.46
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.52
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.32
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.57
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.36
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.79
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.68
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.70
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.91
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.31
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999866864
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.43
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999923366
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.57
 p-value of test no 243                :    0.9949
 
 Sample variance                       :    2.06
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:27.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           5.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89751562.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56068
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 9                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.01
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.64
 p-value of test no 48                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.37
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.90
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.88
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.14
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.76
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.23
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.97
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.33
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.13
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.57
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.75
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.06
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907776
   j =  2                              :            46109
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907954
   j =  2                              :            46017
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.97
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.56
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.62
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.46
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.17
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.31
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    4.56
 p-value of test no 128                :  4.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.70
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.37
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.53
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17170.71
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.92
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.04
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.85
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.56
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.87
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.11
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.05
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.65
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.87
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.33
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.73
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.24
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.67
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.78
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.53
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.06
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.07
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.48
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.56
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.30
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.19
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.41
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.38
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.05
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.58
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.81
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.29
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 181                :    0.9939
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 182                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.11
 p-value of test no 183                :    0.9991    *****
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.94
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.92
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.63
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9740.08
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.29
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.78
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.92
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.60
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.00
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.81
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.59
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000011302
 
 Normal statistic for number of bits   :   0.089
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.85
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000173281
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:59.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  82  LempelZiv, r = 0                0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90767370.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56069
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 6                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.76
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.63
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.13
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.56
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.57
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.21
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.39
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.43
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.53
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.33
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.07
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.81
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.16
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.37
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.46
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908056
   j =  2                              :            45966
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908158
   j =  2                              :            45918
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.46
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.51
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.33
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.71
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.74
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.19
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.86
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.35
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.72
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.99
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.06
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.24
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.01
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.11
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.66
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.92
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.31
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.35
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.25
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.38
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.18
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.63
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.92
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.32
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.82
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.87
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.77
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.35
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.88
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5251.39
 p-value of test no 168                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.99
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.12
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.88
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.31
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.38
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.98
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.32
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.70
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.36
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.64
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.74
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.53
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.43
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.36
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.49
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.01
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.51
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.01
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.31
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.06
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.88
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000021082
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.71
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000029707
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    2.24
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:35.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91783178.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56070
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    6.19
 p-value of test no 38                 :  8.1e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.89
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.37
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.14
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.19
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.93
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.53
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.45
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.38
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.59
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.65
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.59
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.97
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.13
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.37
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.76
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.57
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908052
   j =  2                              :            45971
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908662
   j =  2                              :            45666
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.37
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.37
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.50
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.87
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.55
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.56
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.88
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.59
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.59
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17253.25
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.37
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.71
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.36
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.44
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.99
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.80
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.02
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.22
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.64
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.73
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.99
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.34
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.77
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.20
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.40
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.84
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.15
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.36
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.26
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.95
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.08
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.41
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.54
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.67
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.78
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.82
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.15
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.78
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.16
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.32
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.50
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.98
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
 p-value of test no 205                :    0.9927
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.31
 p-value of test no 207                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 208                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-4
 p-value of test no 209                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    6.31
 p-value of test no 210                :  7.5e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9498.90
 p-value of test no 211                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.30
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.99
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.68
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.26
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.69
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.96
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.15
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.85
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000022357
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.56
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999895562
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.18
 p-value of test no 254                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:31.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          8.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  90  HammingWeight2, r = 0           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92831756.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56071
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.46
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.13
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.25
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.38
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.78
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.77
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.35
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.54
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.13
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.27
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.11
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.87
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.69
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.59
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908053
   j =  2                              :            45966
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46209
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870209
   j =  1                              :        399907585
   j =  2                              :            46203
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.66
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.72
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.83
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.20
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.44
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.39
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.60
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.31
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.03
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.34
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.08
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.88
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.24
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.45
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.72
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.69
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.09
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.49
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.90
 p-value of test no 159                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.13
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.99
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.22
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.79
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.65
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.75
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.58
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.09
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.32
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.91
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.28
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.87
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.72
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.72
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.28
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.56
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.79
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.72
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.85
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.12
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.70
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.89
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4636.44
 p-value of test no 222                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.44
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.73
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.01
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.02
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.64
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.84
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999839369
 
 Normal statistic for number of bits   :   -1.27
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.39
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999857711
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 240                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 241                :    0.9908
 
 Anderson-Darling statistic = A2       :    4.71
 p-value of test no 242                :  4.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.97
 p-value of test no 243                :    0.9985
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:26.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93814796.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56072
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 24                 :    0.9992    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.57
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.32
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.12
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.83
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.52
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.76
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.41
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.81
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.79
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.03
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.76
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.61
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.29
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.17
 p-value of test no 66                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.89
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.82
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908655
   j =  2                              :            45668
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908103
   j =  2                              :            45944
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.22
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.34
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.70
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.39
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.69
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.63
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.74
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.33
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.89
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17195.91
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.23
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.63
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.17
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.69
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.32
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.61
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.91
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.20
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.22
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.63
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.30
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.43
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.67
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.29
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.02
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.77
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.84
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.12
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.99
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.27
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.61
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.08
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.40
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.55
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.99
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.58
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.26
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.01
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.17
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.07
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.49
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.99
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.57
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.84
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 218                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.95
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.89
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.91
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.37
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.81
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.69
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.77
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000128662
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.83
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999858971
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:49.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94863372.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56073
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     347
 p-value of test no 37                 :  4.3e-3
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.18
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.15
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.99
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.51
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.40
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  355.06
 p-value of test no 55                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.61
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.22
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.41
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.19
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.93
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.10
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.68
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908376
   j =  2                              :            45803
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907770
   j =  2                              :            46112
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.77
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.30
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.50
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.45
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.29
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.46
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.93
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.07
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17592.91
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.32
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.51
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.81
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.14
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.70
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.81
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.42
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   38.08
 p-value of test no 155                :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.43
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.81
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.98
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.63
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.08
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.00
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.77
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.18
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.00
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.72
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.00
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.22
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.51
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.21
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.03
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.80
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.48
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.37
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.45
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.95
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.47
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.95
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    2.29
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.55
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-4
 p-value of test no 204                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.02
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.95
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10285.03
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.22
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.18
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.86
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.09
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.36
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.18
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.84
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999908975
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.82
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000011527
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.24
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:03.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95846412.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56074
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.29
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.76
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.57
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.48
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.01
 p-value of test no 51                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.65
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.55
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.60
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.34
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.36
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.32
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-4
 p-value of test no 62                 :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.93
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.40
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.83
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4922.75
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907725
   j =  2                              :            46136
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908747
   j =  2                              :            45616
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.48
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.19
 p-value of test no 120                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.50
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.47
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.85
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.76
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.09
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.02
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.76
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.70
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17228.27
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.35
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.56
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.84
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.72
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.68
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.13
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.15
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.14
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.13
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.77
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.88
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.27
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.33
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.04
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.18
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.58
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.61
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.60
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.01
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.11
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.01
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.01
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.11
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.24
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.22
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.15
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.04
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.49
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.01
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.13
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9735.66
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.23
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.74
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.61
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.82
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.14
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11574.06
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.86
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.65
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000077662
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.42
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999983039
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 251                :  3.3e-4    *****
 
 Anderson-Darling statistic = A2       :    8.59
 p-value of test no 252                :  6.8e-5    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.84
 p-value of test no 253                :  6.2e-5    *****
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:18.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  106  AutoCor, d=3, r=27              6.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96862220.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56075
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.67
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.44
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.51
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.49
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.62
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.25
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.42
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.22
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.37
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.85
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.29
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.03
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.28
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.65
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908461
   j =  2                              :            45762
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45534
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869534
   j =  1                              :        399908933
   j =  2                              :            45532
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 93                 :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 117                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.81
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.38
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.94
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.48
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.73
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.56
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.42
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.22
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17121.21
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.96
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.45
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.07
 p-value of test no 149                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.98
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.57
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.53
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.46
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.76
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.54
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.66
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.64
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.81
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.31
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.33
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.61
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.80
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.56
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.99
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.14
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.44
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.21
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.61
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.71
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.64
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.86
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.48
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.29
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.20
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.23
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.15
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.80
 p-value of test no 198                :    0.9992    *****
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.56
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.12
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.74
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.48
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.95
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.06
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4310.53
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.53
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12165.37
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.03
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.51
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999932309
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.63
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999831827
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:44.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  87  LongestHeadRun, r = 27          0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97878028.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56076
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7497
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    4.31
 p-value of test no 36                 :  6.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     249
 p-value of test no 37                 :    0.9986
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.26
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.05
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.27
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.87
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.22
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.02
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.05
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.96
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.96
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.92
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.46
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.51
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.75
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.16
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908375
   j =  2                              :            45808
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907663
   j =  2                              :            46164
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    6.46
 p-value of test no 108                :  6.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-4
 p-value of test no 110                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 111                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.71
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.10
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.70
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.50
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.93
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.65
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.10
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.45
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.87
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17651.22
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.72
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.70
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.83
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.21
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   72.53
 p-value of test no 151                :  2.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.91
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.96
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.43
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.25
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.50
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.41
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.97
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.40
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.70
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.29
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.41
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.86
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.84
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.09
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.91
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.92
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.37
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.37
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.60
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.55
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.98
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.54
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.47
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.85
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.41
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 213                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.45
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.77
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.16
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.87
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.25
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.25
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.35
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.80
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999860504
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.23
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999883046
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    2.22
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:53.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  52  SampleProd, t = 24              6.3e-4
  75  RandomWalk1 H (L=50, r=25)      2.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98893836.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56077
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    3.89
 p-value of test no 30                 :  9.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.62
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.31
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.24
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.77
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.68
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.96
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.04
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.50
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.57
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.09
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.10
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.58
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.92
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5172.33
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907916
   j =  2                              :            46042
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908291
   j =  2                              :            45850
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.08
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.15
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.33
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.44
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.80
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.25
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.24
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.87
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.17
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.74
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.70
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.11
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.74
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.91
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.24
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.97
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.99
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.64
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.38
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.05
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.37
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.82
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.07
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.69
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.14
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.06
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.37
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.46
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.18
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.26
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.27
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.22
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.18
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.67
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.00
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.00
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.86
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.60
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.75
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.48
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.47
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.96
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.90
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.04
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.77
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.00
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.48
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.64
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.55
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.88
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.24
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.28
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11562.91
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.09
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.97
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999857858
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.82
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000032443
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.82
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 247                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:44.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99909644.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56078
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 16                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.12
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.16
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.53
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.21
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.87
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.74
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.95
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.27
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.08
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.81
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.86
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.88
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908171
   j =  2                              :            45907
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908497
   j =  2                              :            45744
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.14
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.42
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.99
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.80
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.41
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.08
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.71
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.51
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.58
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.65
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.75
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.22
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.37
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.15
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.90
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.12
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.62
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.36
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.08
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.69
 p-value of test no 155                :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.27
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.77
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.70
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.91
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.68
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.78
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.69
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  413.59
 p-value of test no 163                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.38
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.91
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.70
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.92
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.80
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.69
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.90
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.09
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.57
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.29
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.02
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.37
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.34
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.51
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.17
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.12
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.59
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.23
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.92
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.62
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.48
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.88
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.40
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.70
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.88
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000047863
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.69
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999997328
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:35.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100925452.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56079
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.19
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.31
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.48
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.88
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.69
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.64
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.11
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1539.20
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.58
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.85
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.39
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.77
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.72
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45565
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908872
   j =  2                              :            45561
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908369
   j =  2                              :            45808
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.12
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.99
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.84
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.43
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.78
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.48
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.32
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.95
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.73
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.61
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.87
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.74
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.50
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.35
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.48
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.67
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.61
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.97
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.92
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.84
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.63
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.16
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.98
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.03
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.58
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.38
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.97
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.50
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.92
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.56
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4800.15
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.63
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.37
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.71
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.38
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.18
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.99
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.20
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.08
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.12
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.22
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.40
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.50
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.55
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.41
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.14
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 213                :  6.2e-4    *****
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 214                :  9.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10322.56
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.94
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.70
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.35
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.43
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.35
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.32
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.57
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999920819
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.79
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999915593
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:36.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101941260.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56080
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.99
 p-value of test no 48                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.95
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.45
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.96
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.63
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.22
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.87
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.69
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.14
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.22
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.94
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.39
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5237.06
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45399
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869399
   j =  1                              :        399909207
   j =  2                              :            45389
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908144
   j =  2                              :            45919
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.81
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.20
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.89
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.16
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.59
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.88
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.22
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.18
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.47
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.91
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.01
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.02
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.99
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.15
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.22
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.35
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.95
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.61
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.06
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.82
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.66
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.05
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.62
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.45
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.40
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.90
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.02
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.77
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.29
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.09
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.30
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.99
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.54
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.98
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.88
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.33
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.65
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.70
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.69
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.03
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.48
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.68
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.63
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.66
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.21
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.29
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.76
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.15
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.42
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.35
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.26
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.20
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000079840
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.80
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999915806
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.015
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:54.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83394585.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56081
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.83
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.33
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.71
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.13
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.34
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.37
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.37
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.77
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.98
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.64
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.32
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.92
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.32
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46337
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870337
   j =  1                              :        399907327
   j =  2                              :            46335
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907953
   j =  2                              :            46019
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.89
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.66
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.03
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.79
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.44
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.60
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.15
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.74
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.03
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.60
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.56
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.26
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.81
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.38
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.61
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.45
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.95
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.11
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.14
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.16
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.51
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.02
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.79
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.94
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.37
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.22
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.11
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.85
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.94
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.42
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.79
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.25
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.22
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.66
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.56
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.46
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.98
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.72
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.34
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.41
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.64
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.91
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.34
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.50
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.36
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.51
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.27
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.48
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3878.99
 p-value of test no 227                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.79
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.20
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.79
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.81
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999809999
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.08
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999943280
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:01.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84246553.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56082
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 10                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.80
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.08
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.02
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.96
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.88
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.32
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.98
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.00
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.46
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.23
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.19
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.49
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.14
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4866.02
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907957
   j =  2                              :            46017
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908275
   j =  2                              :            45855
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.24
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.96
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.84
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.94
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.63
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.84
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.32
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.44
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.03
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.23
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.35
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.42
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.18
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.36
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.87
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.97
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.35
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.65
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.01
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.63
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.82
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.73
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.92
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.22
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.29
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.05
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.73
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.37
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.49
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.46
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.40
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.28
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.03
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  471.49
 p-value of test no 172                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4818.95
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.73
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.45
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.23
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.90
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.56
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.92
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.26
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.97
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.68
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.02
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.54
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.78
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.47
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.16
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.68
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.11
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999948113
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.58
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999988403
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 238                :    0.91
 
 Sample variance                       :    2.26
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:08.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85458969.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56083
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1497
 p-value of test no 12                 :  2.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334617
   j =  1                              :        599997006
   j =  2                              :             1497
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     977
 p-value of test no 25                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.14
 p-value of test no 33                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.69
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.55
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.05
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.94
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.09
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.87
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.16
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.22
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.28
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.49
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.87
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.77
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.13
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.55
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908129
   j =  2                              :            45934
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908831
   j =  2                              :            45574
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.93
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.56
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.26
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.40
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.82
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.91
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.13
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.63
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.20
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.49
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.56
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.23
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.17
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.00
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   13.54
 p-value of test no 151                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.52
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.24
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.31
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.47
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.09
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.16
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.20
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.67
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.68
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.49
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.50
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.72
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.86
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.80
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.31
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.92
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.23
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.13
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.18
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.70
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.65
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.50
 p-value of test no 176                :  9.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.92
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.85
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.81
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 204                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    5.87
 p-value of test no 206                :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  274.29
 p-value of test no 207                :  3.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.17
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.67
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.71
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.90
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.84
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.91
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.88
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.02
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.01
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999956486
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.37
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000007165
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.98
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.98e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:23.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.1e-4
  23  ClosePairs mNP2S, t = 5         0.9992 
  75  RandomWalk1 H (L=50, r=25)      0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  89  PeriodsInStrings, r = 20        3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86474777.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56084
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7125
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.81
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.29
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.86
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.65
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.16
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.37
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.98
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.80
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7273.84
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.82
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.50
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.54
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.98
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908396
   j =  2                              :            45799
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908289
   j =  2                              :            45854
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.67
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.00
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.32
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.17
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.13
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.88
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.49
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.25
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.48
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.70
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.83
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.89
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.03
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.15
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.54
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.14
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.17
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.58
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.66
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.23
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.54
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.10
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.29
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.66
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.99
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.87
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.28
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.26
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.01
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.05
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.76
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.95
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.59
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.43
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.90
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.18
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.55
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.01
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.28
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.04
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.10
 p-value of test no 189                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.73
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.80
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.10
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.51
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.70
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.01
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.29
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.29
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3841.18
 p-value of test no 228                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12138.07
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.94
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.17
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000078574
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.58
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000008542
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.9909
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:27.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  98  HammingIndep, L=300, r=26       0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87490585.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56085
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.50
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.64
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.60
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.55
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  376.98
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.70
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.90
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.05
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.32
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.13
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.18
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.86
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908097
   j =  2                              :            45947
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.02
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.68
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.61
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.60
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.44
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.97
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.28
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.59
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.54
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.94
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.02
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.97
 p-value of test no 148                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.59
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.41
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.78
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.57
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.31
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.50
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.13
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.45
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.06
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.62
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.00
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.48
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  576.66
 p-value of test no 163                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.60
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.80
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.34
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.49
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.66
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.64
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.67
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.91
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.41
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.34
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.56
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.78
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.43
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.28
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.38
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10232.96
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.21
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.29
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.53
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.82
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.93
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.46
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.23
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000088528
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.06
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000066472
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:23.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88506393.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56086
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    3.73
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.04
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.56
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.55
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.15
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.21
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.27
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.00
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7182.81
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.93
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.10
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.46
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.06
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.13
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908345
   j =  2                              :            45820
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908103
   j =  2                              :            45944
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 103                :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.53
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.99
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.12
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.48
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.78
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.41
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.90
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.31
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.93
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.63
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.12
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.42
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.75
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.89
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.33
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.44
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.22
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.61
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.57
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.00
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.95
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.04
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.70
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.12
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.06
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.19
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.88
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.79
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.85
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.58
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.55
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.54
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.27
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.32
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.82
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.44
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.86
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.50
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.94
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.22
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.98
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.74e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.90
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.56
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.10
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.95
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11591.67
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.13
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.21
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999932156
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.46
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999826784
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:40.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89522201.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56087
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.67
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    4.68
 p-value of test no 39                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.42
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.44
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.62
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.77
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.68
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.89
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.94
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.31
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.40
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.66
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.59
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.48
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.72
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.24
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.14
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907974
   j =  2                              :            46013
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908514
   j =  2                              :            45740
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.72
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.64
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.27
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.82
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.36
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.28
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.04
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.37
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.77
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.20
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.38
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.21
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.24
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.12
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.72
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.63
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.62
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.03
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.97
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.39
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.12
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.30
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.61
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.55
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.59
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.84
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.29
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.84
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.48
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.95
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.79
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.58
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.09
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.85
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.65
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.68
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.07
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.60
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.25
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.88
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.74
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.74
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.35
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.47
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.02
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.83
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.25
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.56
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.54
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.49
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999981986
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.15
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999933590
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:26.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90538009.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56088
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7034
 p-value of test no 20                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.30
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.54
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.97
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.30
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.20
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.07
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.82
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.64
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.12
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.17
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.16
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5217.26
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908478
   j =  2                              :            45755
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 80                 :  4.1e-3
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.96
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.74
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.11
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.32
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.14
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.19
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.50
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.28
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.72
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.63
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.19
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.57
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.44
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.93
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.55
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.11
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.49
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.77
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.74
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.97
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.96
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.68
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.67
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.04
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.38
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.82
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.79
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.47
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.53
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.52
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.48
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  266.09
 p-value of test no 170                :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.33
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.81
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.76
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.52
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.53
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.21
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.62
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.99
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.27
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.90
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.96
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.94
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5138.61
 p-value of test no 226                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.50
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.37
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.88
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.01
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.62
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999919469
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.22
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999962609
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.063
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:33.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91488281.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56089
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.63
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.63
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.52
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.39
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.55
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.77
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.72
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.06
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.14
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.62
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.08
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.14
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.41
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45578
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869578
   j =  1                              :        399908846
   j =  2                              :            45574
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907887
   j =  2                              :            46052
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-3
 p-value of test no 98                 :    0.9983
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.56
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.27
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.85
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.22
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.91
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.91
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.92
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.89
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.81
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.18
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.90
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.65
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.65
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.04
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.19
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.67
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.03
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.60
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.88
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.42
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.88
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.76
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.31
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.06
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.93
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.43
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.81
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.44
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.53
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.82
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.95
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.29
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.95
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.56
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.49
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.39
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.22
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.43
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    5.24
 p-value of test no 187                :  2.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.08
 p-value of test no 188                :    0.9990
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.90
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.06
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.65
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.24
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10263.80
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.57
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.87
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.01
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.13
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.95
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.70
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.80
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000084958
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.58
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999881105
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:41.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92438553.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56090
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7077
 p-value of test no 21                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.75
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.91
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.78
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.23
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.31
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.55
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.21
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.37
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.84
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.81
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 62                 :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   91.46
 p-value of test no 65                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.54
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.14
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.16
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45414
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869414
   j =  1                              :        399909174
   j =  2                              :            45410
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.51
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.48
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.68
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.15
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.89
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.72
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.48
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.03
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17196.22
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.59
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.36
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.37
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.28
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.87
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.07
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.86
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.08
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.82
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.16
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.39
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.51
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.48
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.87
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.35
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.58
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.06
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.86
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.05
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.97
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.57
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.35
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.47
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.60
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.60
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 182                :  9.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 183                :    0.9922
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.04
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.12
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.81
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.55
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.40
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.29
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.44
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.12
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.78
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.57
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.60
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.36
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999971801
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.02
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999996353
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:08.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93356032.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56091
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 27                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     259
 p-value of test no 37                 :    0.9914
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.22
 p-value of test no 46                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.30
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.02
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.94
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.27
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.71
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.91
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.76
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.36
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.32
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.78
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.71
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.16
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.02
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.47
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.53
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908190
   j =  2                              :            45902
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908071
   j =  2                              :            45963
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-4
 p-value of test no 100                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.35
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.98
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.97
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.94
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.87
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.12
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.10
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.86
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.96
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.29
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.82
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.27
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.84
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.51
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.40
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.88
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.85
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.65
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.84
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.41
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.73
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.64
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.27
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.97
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.80
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.92
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.26
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.36
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.54
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.88
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.52
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.71
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.17
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.76
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.50
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.16
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.15
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.79
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.33
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.53
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.67
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.57
 p-value of test no 216                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4699.33
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.20
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4275.01
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.90
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.14
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.36
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.66
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000025936
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.59
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999989009
 
 Normal statistic for number of bits   :  -0.087
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:35.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94404608.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56092
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5259
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.24
 p-value of test no 28                 :  6.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.03
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.37
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.79
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.45
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.99
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.45
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.01
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.04
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.70
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.94
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.70
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.56
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.03
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45650
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869650
   j =  1                              :        399908703
   j =  2                              :            45644
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46224
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870224
   j =  1                              :        399907554
   j =  2                              :            46220
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.66
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.22
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.91
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.66
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.51
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.44
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 128                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.60
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.53
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.68
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17243.35
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.58
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.52
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.05
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.40
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.10
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.24
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.63
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.33
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.65
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.45
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.09
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.45
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.78
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.50
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.33
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.65
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.19
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.56
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.66
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.45
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.69
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.12
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.36
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.50
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.79
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.84
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.26
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.31
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.28
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.92
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.08
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.75
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.58
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.04
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9782.45
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.53
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5036.32
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.53
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.90
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.03
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.19
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.46
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.28
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999823895
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.75
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999931958
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:54.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95649806.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56093
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 11                 :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7497
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9972
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.98
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.55
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.87
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.39
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.56
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.81
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.85
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.10
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.95
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.76
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.30
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.84
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.50
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.12
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46198
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870198
   j =  1                              :        399907605
   j =  2                              :            46196
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908500
   j =  2                              :            45747
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.50
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.68
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.81
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.42
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.01
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.12
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.92
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.02
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.14
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.08
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17673.70
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.54
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.11
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.33
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.68
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.00
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.55
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.03
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.30
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.21
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.14
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.63
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.32
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.15
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.86
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.13
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.20
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.76
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.20
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5213.90
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.46
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.41
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.40
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.37
 p-value of test no 172                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.42
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.01
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.73
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.14
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.70
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.31
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.44
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.52
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.29
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.04
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.96
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.40
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.46
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.39
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.09
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999876590
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.45
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999922277
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    2.01
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:19.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96469006.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56094
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.91
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.91
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.93
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.70
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.95
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.56
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.48
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.15
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.62
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.40
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.12
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.28
 p-value of test no 65                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.24
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.16
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46197
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907609
   j =  2                              :            46191
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45313
 p-value of test no 71                 :    0.9959
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869313
   j =  1                              :        399909376
   j =  2                              :            45309
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.51
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.20
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.60
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.11
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.35
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.09
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.82
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.06
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.72
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.69
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.41
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.23
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.67
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.38
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.52
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.40
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.54
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.12
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.79
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.20
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.60
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.16
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.71
 p-value of test no 164                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.81
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.10
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.44
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.19
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.86
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.18
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.59
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.29
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.76
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.38
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.58
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.47
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.63
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.61
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.60
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.60
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.17
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9923
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.58
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.04
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.60
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3918.49
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.82
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.77
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.06
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.15
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999938309
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.25
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999977204
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:11.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97320987.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56095
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    4.39
 p-value of test no 30                 :  5.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.64
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.16
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.94
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.80
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.79
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.16
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.38
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.65
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.92
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.67
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.42
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.99
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.48
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.31
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908005
   j =  2                              :            45993
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908216
   j =  2                              :            45883
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-3
 p-value of test no 94                 :    0.9986
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 106                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.57
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.89
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.80
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.35
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.14
 p-value of test no 123                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.68
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.34
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.89
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.62
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.06
 p-value of test no 137                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.34
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17654.81
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.16
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.59
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.38
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.46
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.21
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.80
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.39
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.64
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.58
 p-value of test no 156                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.32
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.00
 p-value of test no 158                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.83
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.41
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.12
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.83
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.28
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.50
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.70
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.81
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.85
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.62
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.43
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.02
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.44
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.76
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.00
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.97
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 201                :  8.3e-4    *****
 
 Anderson-Darling statistic = A2       :    7.00
 p-value of test no 202                :  3.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  272.65
 p-value of test no 203                :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.58
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.10
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.30
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.31
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.13
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.87
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3855.29
 p-value of test no 228                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.08
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.41
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.47
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000079441
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.89
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999951962
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-4
 p-value of test no 240                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.70
 p-value of test no 243                :  3.4e-3
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:00.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  88  PeriodsInStrings, r = 0         4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98271259.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56096
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.24
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.53
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.95
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.87
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.91
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.12
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.36
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.30
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.24
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.87
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.13
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.51
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908303
   j =  2                              :            45841
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45491
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869491
   j =  1                              :        399909026
   j =  2                              :            45475
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.40e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.10
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.95
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.75
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.54
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.18
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.92
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.94
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.36
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.32
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.76
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.03
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.36
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.27
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.34
 p-value of test no 147                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.24
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.28
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.56
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.58
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.19
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.73
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.72
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.94
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.48
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.44
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.34
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.93
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.97
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.22
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.78
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.83
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.86
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.54
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.19
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.50
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.06
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.47
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.92
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.40
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.14
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.99
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.92
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.63
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.84
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.95
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.60
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.39
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.28
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.46
 p-value of test no 216                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.25
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.96
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4305.92
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.90
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.96
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.83
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.02
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000058291
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.45
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000192499
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 236                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:04.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99352603.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56097
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.93
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.69
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.61
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.30
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.47
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.36
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.58
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.04
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.21
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.33
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907719
   j =  2                              :            46139
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907908
   j =  2                              :            46040
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 87                 :    0.9919
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9953
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.92
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.96
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.92
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.62
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.04
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.38
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.09
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.27
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.11
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.19
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17162.60
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.41
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.37
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   38.61
 p-value of test no 150                :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.87
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.86
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.41
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.16
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.30
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.17
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.07
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.31
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.83
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.60
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.21
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.75
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.75
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.04
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.55
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.52
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.79
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.64
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.68
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.00
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.17
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.92
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.47
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.03
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.84
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.61
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.48
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.12
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.47
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.64
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.69
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.74
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.04
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.21
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.04
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999964067
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.88
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000152644
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:09.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100466715.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56098
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    2.59
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.80
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.15
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.59
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.34
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.01
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.10
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.01
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.25
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.90
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.39
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.67
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.95
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.67
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4922.03
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45562
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869562
   j =  1                              :        399908877
   j =  2                              :            45560
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908699
   j =  2                              :            45643
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.84
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.73
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.56
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.20
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.96
 p-value of test no 124                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.72
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.65
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.16
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.62
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.01
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.05
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.66
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.05
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.40
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.84
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.69
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.59
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.97
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.00
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.07
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.24
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.79
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.03
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.50
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.47
 p-value of test no 164                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.43
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.36
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.44
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5197.52
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.24
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.81
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.56
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.43
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.41
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.34
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.96
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.81
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.54
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.22
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.01
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.16
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.43
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.66
 p-value of test no 218                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.64
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.91
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.46
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.30
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.94
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.21
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.35
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000143305
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.65
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999994976
 
 Normal statistic for number of bits   :  -0.040
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-3
 p-value of test no 245                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:12.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101482523.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56099
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1221
 p-value of test no 12                 : 1 -  4.2e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334341
   j =  1                              :        599997558
   j =  2                              :             1221
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7100
 p-value of test no 15                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7560
 p-value of test no 20                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.51
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.36
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.42
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.63
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.20
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.20
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.69
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.00
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.98
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.18
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.06
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.68
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.06
 p-value of test no 67                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.41
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907937
   j =  2                              :            46027
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908135
   j =  2                              :            45925
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 94                 :    0.9927
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.56
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.55
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.27
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.26
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.27
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.68
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.47
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.23
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.78
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17192.57
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.03
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.54
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.08
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.31
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.57
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.48
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.40
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.53
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.90
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.84
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.43
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.59
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.76
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.12
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.68
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.69
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.71
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.00
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.97
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.50
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.55
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.03
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.60
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.61
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.55
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.94
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.58
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.83
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.95
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.83
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.71
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.94
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.64
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.14
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.21
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.03
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.27
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.53
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.51
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000055174
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.87
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999912326
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:10.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  4.2e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102531099.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56100
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 12                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.23
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.06
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.19
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.50
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.31
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.20
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6889.50
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.49
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.92
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.40
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.87
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908059
   j =  2                              :            45966
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907924
   j =  2                              :            46032
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.30
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.49
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.78
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.28
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.73
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.94
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.09
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.61
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.95
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.58
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.43
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.80
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.50
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.68
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.49
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.80
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.68
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.33
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.57
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.94
 p-value of test no 161                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.27
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.97
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.22
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.25
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.36
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.21
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.08
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.90
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.68
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.88
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.01
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.28
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.19
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.96
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.11
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.61
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.18
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.09
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 209                :    0.9958
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9750.16
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.62
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.21
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.40
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.57
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.54
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.60
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.63
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.24
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000086494
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.89
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999897365
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 246                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:55.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83427354.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56101
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 12                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4492
 p-value of test no 17                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7554
 p-value of test no 20                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.54
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.11
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.82
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.00
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.52
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.56
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.66
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.59
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1559.96
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.46
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.46
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.47
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.92
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.01
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.19
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45650
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869650
   j =  1                              :        399908709
   j =  2                              :            45632
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908194
   j =  2                              :            45903
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.38
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.41
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.16
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.76
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.93
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.14
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.58
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.81
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.52
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.88
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.38
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.17
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.64
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.87
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.88
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.62
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.81
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.40
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.41
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.96
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.90
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.38
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.67
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.41
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.63
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.05
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.66
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.58
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.52
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.52
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5227.42
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.52
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.71
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.15
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.25
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.55
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.81
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.36
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.34
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.62
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.95
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.96
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.24
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.76
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.49
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.86
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.30
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.35
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.17
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.92
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.70
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999915326
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.86
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000021901
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:09.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84279322.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56102
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7090
 p-value of test no 20                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.12
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 41                 :    0.9970
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.02
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.89
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.88
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.14
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.57
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.31
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.85
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.01
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.81
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.69
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.68
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5187.12
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908010
   j =  2                              :            45989
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45604
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908793
   j =  2                              :            45602
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.34
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.10
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.84
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.51
 p-value of test no 125                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.87
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.58
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.54
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.09
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.62
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.06
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.92
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.51
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.30
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.66
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.64
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.42
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.47
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.11
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.11
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.11
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.43
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.72
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.04
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.95
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.00
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.17
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.19
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.76
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.82
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.06
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.08
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.03
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.07
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.45
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.63
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.96
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.21
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.21
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.96
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.65
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.51
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.72
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.49
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.63
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.11
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.92
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12034.75
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.25
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999895115
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.86
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999980927
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.87
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:34.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84836378.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56103
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.9914
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.63
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.15
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.08
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.15
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.62
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.12
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.08
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.21
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.02
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.21
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.30
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.02
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908730
   j =  2                              :            45629
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908085
   j =  2                              :            45950
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-3
 p-value of test no 98                 :    0.9980
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.27
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.38
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.47
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.28
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.87
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.34
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.14
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.53
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.75
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.26
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17796.20
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.32
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.50
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.65
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.43
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.57
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.21
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.87
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.89
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.90
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.27
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.16
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.40
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.92
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.72
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.94
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.22
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.98
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.26
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.59
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.92
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.31
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.10
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.27
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.83
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.92
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.55
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.51
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.06
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.91
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.95
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.85
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.93
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.94
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.51
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.75
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.96
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.27
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.55
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.50
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.92
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.90
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.86
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999937532
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.57
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999985820
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:06.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85819418.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56104
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.58
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.16
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.19
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.74
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.67
 p-value of test no 52                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.43
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.08
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.05
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.86
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.54
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.48
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.13
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.56
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.50
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908303
   j =  2                              :            45844
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908658
   j =  2                              :            45668
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.41
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.18
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.67
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.35
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.08
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.11
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.06
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   68.52
 p-value of test no 129                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.61
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.91
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.44
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.72
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.90
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.63
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.05
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.47
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.79
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.83
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.10
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.10
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.86
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.13
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.67
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.28
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.46
 p-value of test no 161                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.92
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.78
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.97
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.41
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.96
 p-value of test no 166                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.37
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4741.08
 p-value of test no 168                :    0.9957
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.54
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.51
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.32
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.28
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.10
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.29
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.80
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.52
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.40
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.51
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.73
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.49
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.10
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.62
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.29
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.14
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 223                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4668.08
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.74
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.96
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11513.86
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.45
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000086548
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.74
 p-value of test no 233                :    0.9902
 
 
 -----------------------------------------------
 Total number of bits:  8000000340
 
 Normal statistic for number of bits   : 2.69e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-3
 p-value of test no 245                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:25.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86867994.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56105
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.42
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.32
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.11
 p-value of test no 53                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.61
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.65
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.70
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.69
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.62
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.95
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.46
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.36
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.23
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46298
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870298
   j =  1                              :        399907411
   j =  2                              :            46284
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908756
   j =  2                              :            45616
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.10
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.31
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.21
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.12
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.21
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.85
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.28
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.74
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.83
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.06
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.33
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.18
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.71
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.22
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.05
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.72
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.72
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.67
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.43
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.63
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.64
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.31
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.85
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.75
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.11
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.77
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.93
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.38
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.61
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.11
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.98
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.72
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.08
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.93
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.23
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.01
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.96
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.98
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.51
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.85
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.94
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.30
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.82
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.87
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.26
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.47
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.38
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.53
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.96
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999958889
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.84
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999893045
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:12.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87916570.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56106
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9932
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.62
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.19
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.06
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.87
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.25
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.65
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.97
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.94
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.17
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.14
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.27
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45341
 p-value of test no 70                 :    0.9941
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869341
   j =  1                              :        399909326
   j =  2                              :            45325
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908452
   j =  2                              :            45765
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.87
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.14
 p-value of test no 120                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.76
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.39
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.50
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.99
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.43
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.82
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.50
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.23
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.33
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.50
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.73
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.81
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.40
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.71
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.04
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.03
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.49
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.80
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  195.46
 p-value of test no 159                :  6.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.58
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.24
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.79
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.81
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.69
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.14
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.54
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.09
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.95
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.19
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.62
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.58
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.72
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.19
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.06
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.12
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.49
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.10
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.95
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.54
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.22
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.38
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.78
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.83
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.51
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3897.73
 p-value of test no 228                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.35
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.20
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.55
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999959948
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000041713
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:01.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     6.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88965146.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56107
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.17
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.80
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.09
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.92
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.97
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.56
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.27
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.33
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.37
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.64
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.08
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.61
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.47
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.53
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.96
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5206.50
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46235
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870235
   j =  1                              :        399907535
   j =  2                              :            46225
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907890
   j =  2                              :            46049
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.01
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.52
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.05
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.35
 p-value of test no 122                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.78
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.66
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.33
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.50
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.038
 p-value of test no 134                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.50
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17615.13
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.51
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.37
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.58
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.62
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.40
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.94
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.71
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.73
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.67
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.94
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.35
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.04
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.23
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.96
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  413.25
 p-value of test no 163                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.07
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.12
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.97
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.39
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.46
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.62
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.77
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.03
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.07
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.10
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.97
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.01
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.02
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.12
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.78
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.10
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.17
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.83
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.90
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.16
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.07
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.06
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.48
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.71
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000102424
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.70
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000195070
 
 Normal statistic for number of bits   :    1.54
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9964
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:44.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90144794.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56108
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    3.27
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.57
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.17
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.12
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.56
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.27
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.04
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.99
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.60
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.81
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908290
   j =  2                              :            45852
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.11
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.93
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.69
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.34
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.23
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.14
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.23
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.84
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.30
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.19
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.38
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.86
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.63
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.44
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.66
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.75
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.14
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.08
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.80
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.26
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.54
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.41
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.09
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.13
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.61
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.51
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.08
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.83
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.71
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.18
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.76
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.03
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.95
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.18
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.53
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.09
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.16
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.36
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.75
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.17
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.47
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.36
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.14
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.03
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 213                :  5.2e-5    *****
 
 Anderson-Darling statistic = A2       :    7.25
 p-value of test no 214                :  2.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10464.84
 p-value of test no 215                :  5.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.42
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.07
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.88
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.99
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11522.21
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.22
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.86
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999982292
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.62
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999981086
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.080
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:32.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  91  HammingWeight2, r = 27          5.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91062298.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56109
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.22
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.57
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.54
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.83
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.36
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.94
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.91
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.15
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.40
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.23
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.32
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.06
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.05
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907917
   j =  2                              :            46037
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908715
   j =  2                              :            45635
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.73
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.35
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.54
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.78
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.99
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.67
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.18
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.94
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.42
 p-value of test no 137                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.31
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17643.60
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.06
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.17
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.24
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.32
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.73
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.94
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.14
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.59
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.02
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.33
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.30
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.87
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.04
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.74
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.39
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.81
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.13
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.40
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.58
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.92
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.82
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.10
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.28
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.44
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.52
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.67
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.73
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.49
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.73
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.28
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.10
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.80
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4241.99
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.23
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.37
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.51
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000037831
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.01
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000003241
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    2.24
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:08.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92110874.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56110
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 7                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7530
 p-value of test no 19                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9913
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.75
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.10
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.79
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.38
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.06
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.55
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.55
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.07
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.49
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.31
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.12
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.61
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.75
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.62
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.88
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908179
   j =  2                              :            45906
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908178
   j =  2                              :            45908
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.47
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.26
 p-value of test no 120                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.56
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.77
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.50
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.76
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.88
 p-value of test no 125                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.87
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.02
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.97
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.19
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17634.30
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.84
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.09
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.38
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.77
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.91
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.22
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.65
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.42
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.70
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.87
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.13
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.38
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.03
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.54
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.93
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.81
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.88
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.84
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.95
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.74
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.46
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.37
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.71
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.09
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.35
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.02
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-4
 p-value of test no 194                :    0.9927
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.12
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.52
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.93
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.54
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.15
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.49
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.49
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.46
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.54
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.36
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.62
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.37
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999971165
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.98
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999981851
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.072
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:17.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93061146.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56111
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5681
 p-value of test no 13                 :  2.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.33
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.17
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.85
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.05
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.30
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.13
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.20
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.76
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.43
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.45
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.59
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.68
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.80
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908756
   j =  2                              :            45616
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908008
   j =  2                              :            45993
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 108                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.49
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.29
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.70
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.06
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.19
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.36
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.80
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.24
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.80
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17206.05
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.83
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.74
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.19
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.25
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.89
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.33
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.95
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.42
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.73
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.30
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.36
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.75
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.27
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.87
 p-value of test no 160                :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.73
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.06
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.46
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.31
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.87
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.85
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.48
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.26
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.73
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.02
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.75
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.86
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.42
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.42
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.42
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.98
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.73
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.51
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.13
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.06
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.89
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.60
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4663.45
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.16
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.05
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.44
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.17
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.07
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999977792
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.58
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999951929
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:08.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         2.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94076954.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56112
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 11                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    5.51
 p-value of test no 33                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.15
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.21
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.26
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.16
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.53
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.76
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.47
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.14
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.64
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.01
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.29
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.89
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.86
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908158
   j =  2                              :            45918
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46211
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907581
   j =  2                              :            46205
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.50
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.53
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.17
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.22
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.68
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.06
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.17
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.78
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.22
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.19
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.84
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.35
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.28
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.37
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.67
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.91
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.45
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.88
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.72
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.59
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.49
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.64
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.00
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.40
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.51
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.16
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.83
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.41
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.93
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.12
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5240.01
 p-value of test no 168                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.53
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.09
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.57
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.29
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.50
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.94
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.53
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.61
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.09
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.76
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.50
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.35
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.80
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10230.44
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.01
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.10
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.59
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.95
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.55
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.84
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.97
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000056116
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.52
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999823733
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95092762.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56113
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.34
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    4.28
 p-value of test no 32                 :  6.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.17
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.81
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.73
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.92
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.95
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.98
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.94
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.71
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.61
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.01
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.74
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6803.02
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.73
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.05
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.80
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.85
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45689
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908625
   j =  2                              :            45683
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908626
   j =  2                              :            45684
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
 p-value of test no 73                 :    0.9980
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9933
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-5
 p-value of test no 113                :    0.9901
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 114                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.28
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.21
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.52
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.79
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.99
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.91
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.09
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.57
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.55
 p-value of test no 135                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.29
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.33
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.06
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.50
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.99
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.67
 p-value of test no 149                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.98
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.76
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.09
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.20
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.40
 p-value of test no 155                :    0.9900
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.20
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.20
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.18
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.16
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.79
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.16
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.84
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.70
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.67
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.05
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.07
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.51
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.09
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.95
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.48
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.90
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.77
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.35
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.64
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.24
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.95
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.16
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.41
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
 p-value of test no 213                :    0.9982
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9641.51
 p-value of test no 215                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.25
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.10
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.56
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.33
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.00
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.97
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.08
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000121858
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.99
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999914288
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:52.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96075802.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56114
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 11                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9934
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.02
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.42
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.72
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.74
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.64
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.49
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.83
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.19
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.59
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.18
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.72
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.31
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.03
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.43
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.79
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907812
   j =  2                              :            46085
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908415
   j =  2                              :            45788
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.05
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.31
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.84
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.23
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.69
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.73
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.39
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.40
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.45
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.67
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.86
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.58
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.29
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.47
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.17
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.59
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.42
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.32
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.55
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.51
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.99
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.45
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.35
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.51
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.14
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.76
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.93
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.92
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.87
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.71
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.44
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.76
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.40
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.53
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.58
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.68
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.89
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.87
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.61
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.81
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.47
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.83
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.42
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.05
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.56
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.48
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.60
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.72
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.84
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000030766
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.66
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000183814
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    2.35
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:32.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97091610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56115
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.57
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.69
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.28
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.24
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.36
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.95
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.09
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.92
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.34
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.21
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.35
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.51
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908207
   j =  2                              :            45895
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908604
   j =  2                              :            45692
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.16
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.99
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.29
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.15
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.34
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.45
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.77
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.07
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.86
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.63
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.04
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.94
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.66
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.17
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.45
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.12
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.33
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.16
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.03
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.92
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.33
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.15
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.47
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.18
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.38
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.23
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.84
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.20
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.24
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.11
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4753.15
 p-value of test no 168                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.08
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.03
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.69
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.93
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.12
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.29
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.01
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.43
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 186                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.12
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.89
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.32
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.67
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.26
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.19
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.46
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.63
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.28
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.33
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000066334
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.49
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000170074
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:49.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98107418.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56116
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5570
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.34
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.45
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.18
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.47
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.67
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7339.35
 p-value of test no 57                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.73
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.61
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.76
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.00
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.81
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45598
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869598
   j =  1                              :        399908806
   j =  2                              :            45594
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907679
   j =  2                              :            46156
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 87                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.49
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.20
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.18
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.02
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.99
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.67
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17475.30
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.56
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.03
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.75
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.60
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.26
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.71
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.17
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.22
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.03
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.97
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.99
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.08
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.16
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.06
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.59
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.50
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.11
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.55
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.23
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.08
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5245.44
 p-value of test no 168                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.08
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.64
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.32
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.38
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.86
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.33
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.20
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.93
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.95
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.09
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.45
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.00
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.46
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.89
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.15
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.09
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.98
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3923.33
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.78
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.41
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.93
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000027400
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.93
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000049483
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9934
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:58.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99123226.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56117
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 10                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 12                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7106
 p-value of test no 21                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     822
 p-value of test no 25                 :    0.9956
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     659
 p-value of test no 31                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.47
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.02
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.99
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.26
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.37
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.12
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.69
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.88
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7289.10
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.17
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.12
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.61
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.79
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908270
   j =  2                              :            45865
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908130
   j =  2                              :            45932
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.66
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.55
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.45
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.29
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.11
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.07
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.34
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.75
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.16
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.63
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.04
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.95
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.09
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.82
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.15
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.20
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.13
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.78
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.80
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.80
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.97
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.66
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.79
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.73
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.69
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.52
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.90
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.14
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.09
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.00
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.95
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.80
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.86
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.77
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.98
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.25
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.11
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.97
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.72
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.65
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.19
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.03
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.38
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.15
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.93
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.29
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.27
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.61
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.71
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.06
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.00
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.87
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.66
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999861986
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.31
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999945338
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:09.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           5.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100139034.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56118
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.07
 p-value of test no 22                 :  2.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    5.17
 p-value of test no 30                 :  2.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     657
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.9913
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 42                 :    0.9982
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.65
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.20
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.85
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.47
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.76
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.35
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.00
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.23
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.12
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.98
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.54
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.36
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.52
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907901
   j =  2                              :            46045
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908443
   j =  2                              :            45777
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.50
 p-value of test no 116                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.42
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.25
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.32
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.17
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.84
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.34
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.00
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.30
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.77
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.05
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.80
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.21
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.90
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.20
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.94
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.43
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.78
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.80
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.16
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.64
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.57
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.23
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.50
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.35
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.89
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.77
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.85
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.76
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.44
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.39
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.64
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.94
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.79
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.72
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.88
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.19
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.96
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.48
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.23
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
 p-value of test no 181                :    0.9953
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.07
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.61
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.46
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.99
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.33
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.94
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.63
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.20
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.80
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.10
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.71
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.94
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000015007
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.69
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000046348
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.86
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:33.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101154842.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56119
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    4.64
 p-value of test no 45                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.58
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.32
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.17
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.42
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.55
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.80
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.11
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.78
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.62
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.73
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.04
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.29
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.22
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.40
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907726
   j =  2                              :            46131
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908692
   j =  2                              :            45645
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.37
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.87
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.17
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.52
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.99
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.27
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.80
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.63
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.74
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.29
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.58
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.32
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.15
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.25
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.58
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.71
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.03
 p-value of test no 155                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.29
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.95
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.62
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.26
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.91
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.08
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.06
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.46
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.03
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.50
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.47
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.39
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.28
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.24
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.12
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.13
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.21
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.26
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.02
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.79
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.33
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.84
 p-value of test no 207                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.09
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.36
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 221                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.79
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.25
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.68
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.93
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.96
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.22
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.54
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999968744
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.90
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000048535
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.90
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:53.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102170650.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56120
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 34                 :    0.9976
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.42
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.63
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.17
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.71
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.87
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.71
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1541.41
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6862.96
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.90
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.52
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.51
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.63
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.05
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908081
   j =  2                              :            45955
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-6
 p-value of test no 113                :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.21
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.72
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.01
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.24
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.46
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.40
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.12
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.92
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17145.55
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.99
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.37
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.22
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.02
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.54
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.61
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.55
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.11
 p-value of test no 157                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.15
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.70
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.40
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.02
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.66
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  422.90
 p-value of test no 163                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.58
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.35
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.10
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.58
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.32
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.03
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.72
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.12
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.20
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.65
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.62
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.67
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.50
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.11
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.59
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.78
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10241.25
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.54
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.15
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.44
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.38
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.66
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.32
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.22
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.19
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000003541
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.11
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999986237
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:38.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83460123.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56121
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.06
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.87
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.28
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.58
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.87
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.36
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.28
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.92
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.63
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.20
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.53
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.79
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.67
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908387
   j =  2                              :            45802
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908194
   j =  2                              :            45897
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
 p-value of test no 76                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.38
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.88
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.16
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.45
 p-value of test no 122                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.02
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.64
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.41
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.21
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.91
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.04
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.66
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.14
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.05
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.82
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.33
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.79
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.50
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.73
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.46
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.25
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.28
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.43
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.32
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.18
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.44
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.70
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.76
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.52
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.03
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.64
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.04
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.65
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.13
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.06
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.52
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.47
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.30
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.94
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.43
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10252.07
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.63
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.69
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.84
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.46
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.64
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.62
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.75
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.04
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000052294
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.07
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999979988
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.068
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.43
 p-value of test no 253                :  7.5e-3
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:22.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83984411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56122
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 11                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.38
 p-value of test no 22                 :  2.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 39                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.78
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.18
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.08
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.54
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.18
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.39
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.07
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.09
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.35
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.37
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.76
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907915
   j =  2                              :            46038
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907941
   j =  2                              :            46022
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.29
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.89
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.82
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.51
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.35
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.77
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.71
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.65
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17842.06
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.25
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.74
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.43
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.45
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.23
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.79
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.58
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.19
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.37
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.29
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.16
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.71
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.69
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.38
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.19
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.58
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.92
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.89
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.58
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.03
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.32
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.94
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.41
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.59
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.30
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.23
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.77
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.88
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.15
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.39
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.17
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.08
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.50
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.14
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.79
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.01
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.72
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.87
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12113.09
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.81
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000009754
 
 Normal statistic for number of bits   :   0.077
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.95
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000061297
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    2.14
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:10.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84803611.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56123
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 9                  :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 21                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     259
 p-value of test no 37                 :    0.9914
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.74
 p-value of test no 40                 :  4.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.70
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.35
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.96
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.11
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.43
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.32
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.58
 p-value of test no 53                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.77
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.49
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1541.90
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.07
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.64
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.04
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.49
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.27
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45618
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908767
   j =  2                              :            45612
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46308
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870308
   j =  1                              :        399907388
   j =  2                              :            46300
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.08
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.57
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.23
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.05
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.92
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.52
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 130                :  9.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 132                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.33
 p-value of test no 133                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.15
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.87
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.43
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.37
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.04
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.53
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.77
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.24
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.44
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.00
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.20
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.41
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.36
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.98
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.92
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.86
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.32
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.69
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.04
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.02
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.19
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.11
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.03
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.25
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.29
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.72
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.80
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.25
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.46
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.39
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 180                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.63
 p-value of test no 183                :  4.3e-3
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.71
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.88
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.81
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.00
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.22
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.92
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.44
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.69
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.75
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.83
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.65
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999844655
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.92
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000107629
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:02.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           8.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85917723.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56124
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.45
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.23
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.20
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.98
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.38
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.42
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.64
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.27
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.15
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.18
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.71
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.30
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.07
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.62
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.88
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45523
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908955
   j =  2                              :            45521
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908132
   j =  2                              :            45931
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.02
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.70
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.54
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.17
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.67
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.56
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.75
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.16
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17461.07
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.67
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.87
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.17
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.46
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.90
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.27
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.67
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.92
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.23
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.65
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.96
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.98
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.40
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.77
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.02
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.06
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.39
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.02
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.32
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.57
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.50
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.35
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.83
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.67
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.52
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.52
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.33
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.26
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.77
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.98
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.20
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.12
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.34
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4689.42
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5042.68
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4299.38
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.75
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.27
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.78
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.39
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000055291
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.47
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000063724
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    2.03
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:20.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86933531.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56125
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997161
   j =  2                              :             1418
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7109
 p-value of test no 21                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.03
 p-value of test no 46                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.39
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.78
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.40
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.14
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.41
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.36
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.12
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.76
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.65
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 58                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.63
 p-value of test no 61                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 62                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.44
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.61
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.40
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4842.40
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46143
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870143
   j =  1                              :        399907719
   j =  2                              :            46133
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46207
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870207
   j =  1                              :        399907587
   j =  2                              :            46205
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 3.37e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.75
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.66
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.76
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.61
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.33
 p-value of test no 125                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.20
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.30
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.56
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.95
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.60
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.33
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.83
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.70
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.01
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.80
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.46
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.05
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.52
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.04
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.56
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.81
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.31
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.01
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.82
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.98
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.23
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.06
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.03
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.16
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.00
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.36
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.25
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.45
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.01
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.13
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 185                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.02
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.14
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.42
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.11
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.20
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.74
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.96
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.37
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.98
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.39
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.64
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000212860
 
 Normal statistic for number of bits   :    1.68
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.73
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999823613
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.083
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.38e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:52.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88047643.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56126
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 12                 :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.32
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.00
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.53
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.99
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.24
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.28
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.69
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.32
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.06
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.06
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.79
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.30
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.58
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.62
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.58
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908708
   j =  2                              :            45637
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46233
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870233
   j =  1                              :        399907538
   j =  2                              :            46225
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.18
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.79
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.40
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.12
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.98
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.69
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.11
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.97
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.20
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.27
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.14
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.90
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.36
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.25
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.74
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.32
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.83
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.79
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.82
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.11
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.36
 p-value of test no 157                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.11
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.85
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.34
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.49
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.56
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.87
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.28
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.77
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.46
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.91
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.54
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.91
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.87
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.91
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.64
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.31
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.23
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.66
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.89
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.91
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 188                :    0.96
 
 Sample variance                       :    2.06
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.80
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.76
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.27
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.47
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.68
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.47
 p-value of test no 216                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.02
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.73
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.00
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.52
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.32
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12087.26
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.07
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000168838
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000067906
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9962
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:42.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88997915.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56127
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.01
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.18
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.25
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.03
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.06
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.21
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.37
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.77
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.34
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.54
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.98
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.05
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.22
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.50
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908236
   j =  2                              :            45876
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-3
 p-value of test no 87                 :    0.9989
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9945
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  9.5e-3
 
 Anderson-Darling statistic = A2       :    5.12
 p-value of test no 92                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.10
 p-value of test no 119                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.77
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.31
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.17
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.86
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.72
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.46
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.83
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17500.37
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.09
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.17
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.39
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.65
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.59
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.76
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.73
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.01
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.82
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.62
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.49
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.00
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.50
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.87
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.49
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   93.18
 p-value of test no 164                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.06
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.26
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.55
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.77
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.58
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.22
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.21
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.20
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5211.96
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.98
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.30
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.85
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.39
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.29
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.81
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10304.23
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.55
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.42
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.91
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.75
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.45
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11594.11
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.44
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999999515
 
 Normal statistic for number of bits   : -3.83e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.94
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000039604
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.068
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:13.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90046491.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56128
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 6                  :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    4.86
 p-value of test no 30                 :  3.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.83
 p-value of test no 47                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.34
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.95
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.24
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.31
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.89
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.65
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.02
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.06
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.89
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 62                 :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    5.00
 p-value of test no 64                 :  3.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   34.68
 p-value of test no 65                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.39
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.08
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.95
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907983
   j =  2                              :            46007
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908451
   j =  2                              :            45773
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.28
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.42
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.27
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.13
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.58
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.08
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.05
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.49
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.58
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17561.87
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.11
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.18
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.94
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.87
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.90
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.12
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.57
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.70
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.84
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.66
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.18
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.97
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.39
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.86
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.11
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.58
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.93
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.70
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.93
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.92
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.87
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.53
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.16
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.58
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.36
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.82
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.88
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.07
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.97
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.57
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.35
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.31
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.67
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.39
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.95
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.81
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.25
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.34
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.16
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999923558
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.72
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000134107
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:56.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91095067.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56129
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.94
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.43
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.38
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.83
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.46
 p-value of test no 52                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.33
 p-value of test no 53                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.72
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.15
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.51
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6838.79
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.00
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.44
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.44
 p-value of test no 66                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.03
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.43
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908059
   j =  2                              :            45969
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908343
   j =  2                              :            45821
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-3
 p-value of test no 97                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.40
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.36
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   71.77
 p-value of test no 123                :  5.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.83
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.93
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.89
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.83
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.94
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.03
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.92
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.48
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.06
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.32
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.03
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.95
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.20
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.19
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.32
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.81
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.97
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.83
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.63
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.40
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.87
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.56
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.31
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.33
 p-value of test no 165                :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.78
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.06
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.40
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.99
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.31
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.08
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.39
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.62
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.49
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.42
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.13
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.79
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.07
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.70
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9719.32
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.51
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.44
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.62
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.47
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.74
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.31
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.62
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999931076
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.64
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999936806
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:04.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           5.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92241947.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56130
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    4.15
 p-value of test no 38                 :  7.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.75
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.70
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.30
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.50
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.67
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.71
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.11
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.73
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.44
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.64
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  529.67
 p-value of test no 55                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.96
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.00
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.63
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.72
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.97
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.56
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5117.53
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908627
   j =  2                              :            45676
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45516
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869516
   j =  1                              :        399908974
   j =  2                              :            45504
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.20
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.42
 p-value of test no 122                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.22
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.37
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.53
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.31
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.97
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.27
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.49
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.22
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.14
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.20
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.84
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.05
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.21
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.24
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.12
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.36
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.39
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.06
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.40
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.05
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.94
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.45
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.26
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.69
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.18
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.66
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.91
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.14
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.19
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.41
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.48
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.46
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.61
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.23
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.87
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.38
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  253.77
 p-value of test no 207                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.80
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.18
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.27
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.39
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.39
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.00
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.06
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.78
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.91
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999941594
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.43
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000059962
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:29.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93224987.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56131
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.70
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.95
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.56
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.36
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.87
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.95
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.48
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.47
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6935.37
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.10
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.22
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.85
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.95
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.07
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908201
   j =  2                              :            45892
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908487
   j =  2                              :            45755
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.83
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.65
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.42
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.01
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.21
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.22
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.44
 p-value of test no 125                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.18
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.79
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.84
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.92
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.85
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 143                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17759.37
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.31
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.91
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.93
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.42
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.57
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.20
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.24
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.14
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.23
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.23
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.17
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.33
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.69
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.13
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.62
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.80
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.48
 p-value of test no 165                :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.88
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.97
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.80
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.42
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.99
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.34
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.35
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.00
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.79
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.47
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.55
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.21
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 205                :  9.4e-4    *****
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.55
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.67
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.89
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.23
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.83
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.02
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.85
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12088.61
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.78
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.59
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999806750
 
 Normal statistic for number of bits   :   -1.53
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.70
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999930878
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:05.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94273563.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56132
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 11                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.41
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.86
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.89
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.50
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.42
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.02
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.85
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.04
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.75
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.12
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.81
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.90
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908033
   j =  2                              :            45979
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907937
   j =  2                              :            46027
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.85
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.68
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.23
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.03
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.16
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.27
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.18
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.67
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.06
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17722.88
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.04
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.86
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.83
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.94
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.75
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.99
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.07
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.96
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.77
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.78
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.09
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.14
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.36
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.55
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.08
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.09
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.36
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.82
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.75
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.89
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.29
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.05
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.03
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.47
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.45
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.87
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.06
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.35
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.96
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.12
 p-value of test no 184                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.76
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   44.00
 p-value of test no 199                :  2.8e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.21
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
 p-value of test no 205                :    0.9975
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.38
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9812.81
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.96
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.89
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.52
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.52
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.54
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.25
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.62
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.93
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000053014
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.03
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999900848
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:54.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  87  LongestHeadRun, r = 27          2.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95354907.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56133
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 7                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 11                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.50
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.51
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.11
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.74
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.40
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.07
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.10
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.69
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.45
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.51
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.78
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.30
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.52
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.01
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.91
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46151
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870151
   j =  1                              :        399907701
   j =  2                              :            46145
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45565
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908877
   j =  2                              :            45551
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 106                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.05
 p-value of test no 117                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.86
 p-value of test no 120                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.78
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.03
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.21
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.68
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.40
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.90
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.20
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.87
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.66
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.58
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.00
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.73
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.77
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.33
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.21
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.20
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.44
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.80
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.80
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.58
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.17
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.20
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.30
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.39
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.15
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.72
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.03
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.58
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.41
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.46
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.66
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.72
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.04
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.84
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.66
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.41
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.14
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.30
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.88
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.50
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.80
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.21
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.24
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.15
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.35
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.40
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.34
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.30
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.98
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000011419
 
 Normal statistic for number of bits   :   0.090
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.09
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999977837
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:41.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96239643.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56134
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4491
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.63
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.91
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.99
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.55
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.32
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.36
 p-value of test no 52                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.69
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.07
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.80
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.47
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.90
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.48
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.83
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.91
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908373
   j =  2                              :            45806
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908334
   j =  2                              :            45827
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.54e-4
 p-value of test no 110                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.38
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.38
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.21
 p-value of test no 122                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.89
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.70
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.36
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.19
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.00
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17211.42
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.37
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.71
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.41
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.72
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.66
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.04
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.69
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.85
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.40
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.81
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.94
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.21
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.08
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.57
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.89
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.81
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.03
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.16
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.98
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.41
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.87
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.58
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.41
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.17
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.72
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.37
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.86
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.62
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.11
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.11
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.39
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.44
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.14
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.33
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.73
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.13
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.65
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.15
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.12
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.87
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.00
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999896147
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999946874
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:42.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97288206.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56135
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.99
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.03
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.85
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.01
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.58
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.16
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.22
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6889.68
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.20
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.60
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.41
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.96
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908046
   j =  2                              :            45971
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908697
   j =  2                              :            45650
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.01
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.61
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.94
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.32
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.04
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.83
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.91
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.40
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.05
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.70
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.11
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.47
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.76
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.40
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.77
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.79
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.10
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.85
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.83
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.19
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.67
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.17
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.87
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.83
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.82
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.93
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.27
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.44
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.09
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.16
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.12
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.50
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.20
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.72
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.47
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.49
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.80
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.67
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.22
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.32
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.33
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.69
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.09
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.86
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.27
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.06
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3951.59
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.53
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.72
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.60
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000029806
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.45
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000109090
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-4
 p-value of test no 235                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 236                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    6.18
 p-value of test no 237                :  8.7e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.67
 p-value of test no 238                :  1.2e-4    *****
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    2.20
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:58.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  103  AutoCor, d=1, r=0               1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98369550.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56136
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     252
 p-value of test no 37                 :    0.9975
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.79
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.34
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.39
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.46
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.88
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.82
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.35
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.57
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.84
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.04
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.96
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.26
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5146.22
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907859
   j =  2                              :            46057
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46292
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870292
   j =  1                              :        399907419
   j =  2                              :            46286
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
 p-value of test no 109                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-5
 p-value of test no 110                :    0.9941
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 111                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.70
 p-value of test no 120                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.62
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.05
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.98
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.13
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.58
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17304.45
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.89
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.76
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.23
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.55
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.12
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.86
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.33
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.47
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.16
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.38
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.73
 p-value of test no 157                :    0.9974
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.75
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.61
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.50
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.76
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.36
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.72
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.14
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.96
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.57
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.93
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4657.81
 p-value of test no 168                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.92
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.42
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.34
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.26
 p-value of test no 172                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.26
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.52
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.65
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.35
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.80
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.89
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.30
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10255.91
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.70
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.69
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.44
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.57
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.90
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.76
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.20
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.55
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000104542
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.50
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000059845
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:37.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 J (L=10000, r=0)    0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99450894.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56137
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.63
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.79
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.50
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.35
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.73
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.47
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.55
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.87
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.38
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.29
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.88
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.65
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46294
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907414
   j =  2                              :            46290
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908336
   j =  2                              :            45826
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.98
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.05
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.74
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.40
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.54
 p-value of test no 123                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.82
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.27
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.78
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   93.68
 p-value of test no 141                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17145.06
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.09
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.87
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.24
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.51
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.23
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.34
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.57
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.37
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.08
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.93
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.88
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.50
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.63
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.30
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.41
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.17
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.24
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.28
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.04
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.40
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.82
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.69
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.47
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.01
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.17
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.20
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.85
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.34
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.53
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.34
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.90
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.80
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.45
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.12
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.66
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.86
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.99
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.98
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.79
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.13
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.80
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.88
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000101797
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.69
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000029803
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.078
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.76e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:56.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100302862.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56138
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4487
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     113
 p-value of test no 43                 :    0.9990    *****
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.67
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.14
 p-value of test no 47                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.90
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.63
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.30
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.80
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.83
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  182.31
 p-value of test no 54                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.31
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.06
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.31
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.93
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.72
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.29
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.87
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907976
   j =  2                              :            46006
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.90
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.77
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.61
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.09
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.91
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.29
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.14
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.67
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17654.40
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.65
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.92
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.32
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.42
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.48
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.80
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.31
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.58
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.63
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.41
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.92
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.15
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.32
 p-value of test no 160                :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.78
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.71
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.70
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.51
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.93
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.65
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.10
 p-value of test no 167                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.19
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.95
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.09
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.64
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.17
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.80
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.52
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.64
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.70
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.79
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.79
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.96
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9788.39
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.97e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.20
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.37
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.54
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.65
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.22
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.71
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.16
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999849857
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.28
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000093889
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 240                :  3.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    5.71
 p-value of test no 242                :  1.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.03
 p-value of test no 243                :    0.9988
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.089
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.88
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:59.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       0.9990 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101580814.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56139
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1538
 p-value of test no 11                 :  2.1e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334658
   j =  1                              :        599996924
   j =  2                              :             1538
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.14
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.38
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.37
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.54
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.13
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.50
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.95
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.75
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1336.70
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6738.53
 p-value of test no 57                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.21
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.94
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.71
 p-value of test no 66                 :  5.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.80
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.86
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45451
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869451
   j =  1                              :        399909100
   j =  2                              :            45447
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908350
   j =  2                              :            45819
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.27
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.30
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.73
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.37
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.33
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.06
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.85
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.15
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.49
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.10
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17634.39
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.43
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.71
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.06
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.64
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.28
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.57
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.18
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.26
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.51
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.25
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.85
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.21
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.80
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.64
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.74
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.71
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.31
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.18
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.92
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.35
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.77
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.97
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.31
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.51
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.55
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.45
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.98
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.33
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.21
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.81
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.02
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.52
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.23
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.61
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.49
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.28
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.06
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.11
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.49
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.24
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.19
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000014149
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.40
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000048604
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:28.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           2.1e-6
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102465550.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56140
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 12                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.38
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.32
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.90
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.50
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.96
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.95
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.61
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.49
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.20
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.10
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.06
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.82
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.74
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.17
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5270.98
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908629
   j =  2                              :            45684
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907789
   j =  2                              :            46104
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
 p-value of test no 80                 :    0.9965
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9924
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.77
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.86
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.55
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.27
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.11
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.35
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.27
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.40
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.56
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.35
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.59
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.41
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.28
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.49
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.13
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.16
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.96
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.52
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.03
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.34
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.78
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.72
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.48
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.20
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.75
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.49
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.36
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.08
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.21
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.63
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.66
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.56
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.63
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.39
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.98
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.99
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.56
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.51
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.14
 p-value of test no 176                :    0.9944
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.21
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.67
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 205                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.17
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.28
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.40
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.28
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5114.05
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.15
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.97
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12089.82
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.23
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.16
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000004483
 
 Normal statistic for number of bits   :   0.035
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.00
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999847799
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.88
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:06.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83492892.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56141
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.95
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.59
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.20
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.42
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.76
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.50
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.28
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6840.19
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.03
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.64
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.89
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.37
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5209.23
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908306
   j =  2                              :            45844
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907861
   j =  2                              :            46065
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-4
 p-value of test no 112                :  6.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-5
 p-value of test no 113                :    0.9933
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 114                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.41
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.61
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.63
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.42
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.74
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.31
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.03
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.86
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.61
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.57
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.43
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.99
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.39
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.98
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.87
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.56
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.70
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.78
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.86
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.14
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.63
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.50
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.57
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.80
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.53
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.85
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.42
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.66
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.82
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.57
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.38
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.08
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.50
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.75
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  300.08
 p-value of test no 172                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4801.55
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.69
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.56
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.32
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.77
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.81
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.87
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.29
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.55
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.17
 p-value of test no 216                :  7.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.28
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.11
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.70
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.82
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.73
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.86
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.18
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999947687
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.31
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999895877
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:56.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9994 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  92  HammingCorr, L = 30             7.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83623964.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56142
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.39
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.39
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.02
 p-value of test no 49                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.30
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.61
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.83
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.75
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.56
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.93
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7190.03
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.33
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.77
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.67
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.17
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.56
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908480
   j =  2                              :            45760
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908343
   j =  2                              :            45821
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 83                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.19
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.12
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.58
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.68
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.62
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.43
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.64
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.16
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.77
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.24
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.51
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.65
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.33
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.96
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.06
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.60
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.11
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.42
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.16
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.96
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.11
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.08
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.72
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.02
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.21
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.13
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.20
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.98
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.92
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.94
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.82
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.70
 p-value of test no 166                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.10
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.41
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.63
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.43
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.09
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.54
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.60
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.16
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.65
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.85
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.58
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.82
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.69
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.54
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.94
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.18
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.29
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.89
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.47
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000078340
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.93
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000000268
 
 Normal statistic for number of bits   : 2.12e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.069
 p-value of test no 238                :    0.53
 
 Sample variance                       :    2.32
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:42.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84639772.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56143
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.74
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.66
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.37
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.55
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.36
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.14
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.42
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.96
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.03
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.33
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.52
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.34
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4882.03
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908369
   j =  2                              :            45811
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908447
   j =  2                              :            45775
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 73                 :    0.9943
 
 Anderson-Darling statistic = A2       :    4.84
 p-value of test no 74                 :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9987
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 81                 :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9975
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.54
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.16
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.63
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.60
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.58
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.88
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.78
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.58
 p-value of test no 135                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.70
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.68
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.93
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.83
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.80
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.79
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.24
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.10
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.35
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.88
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.12
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.33
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.26
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.53
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.45
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.41
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.53
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.91
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.08
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.41
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.90
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.40
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.55
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.66
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.72
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.29
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.13
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.93
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.70
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.94
 p-value of test no 176                :  5.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.34
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.08
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.73
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.97
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.96
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.03
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.07
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.83
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.45
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.32
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.43
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.38
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999997493
 
 Normal statistic for number of bits   :  -0.020
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.81
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000024697
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    2.31
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:09.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85688348.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56144
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    3.20
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.04
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.19
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.44
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.61
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.67
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.57
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.29
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.44
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6929.74
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.09
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.93
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.82
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.82
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.72
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908303
   j =  2                              :            45844
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908173
   j =  2                              :            45909
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.90
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.15
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.67
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.15
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.44
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.82
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   98.16
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.37
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.25
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.99
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.52
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.01
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.69
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.43
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.81
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.17
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.87
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.96
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.05
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.15
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.30
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.03
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.14
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.06
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.18
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.38
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.80
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.42
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  299.41
 p-value of test no 169                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.03
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.83
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.33
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.71
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.87
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.42
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.45
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.95
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.63
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.07
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4685.16
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.93
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.62
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.19
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.92
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.63
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000071350
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.20
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000115390
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 240                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:39.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86704156.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56145
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.36
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.01
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.51
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.39
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.46
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.68
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.63
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.75
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.67
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.94
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.75
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.06
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5228.44
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46295
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870295
   j =  1                              :        399907415
   j =  2                              :            46285
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908652
   j =  2                              :            45665
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.34
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.55
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.73
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.72
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.83
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.20
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.02
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.95
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.62
 p-value of test no 137                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.73
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-4
 p-value of test no 142                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17967.99
 p-value of test no 145                :  2.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.07
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.61
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.16
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.33
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.42
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.25
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.91
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.07
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.62
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.37
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.36
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.88
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.30
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.60
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.48
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.51
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.32
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.01
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.50
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.71
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.25
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  267.46
 p-value of test no 170                :  1.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.81
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.85
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.69
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.29
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.64
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.16
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.98
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.38
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9786.07
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.50
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.67
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.85
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3916.55
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.58
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.53
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.50
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.69
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000027649
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.47
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000081217
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 247                :    0.9956
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:29.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87687196.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56146
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    5.64
 p-value of test no 39                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.46
 p-value of test no 41                 :  5.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.55
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.04
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.59
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.91
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.56
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.99
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.59
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.10
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.25
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7295.72
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.10
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.53
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.59
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.58
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908585
   j =  2                              :            45700
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908491
   j =  2                              :            45750
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.80
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.80
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.04
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.37
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.89
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.56
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.99
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.92
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.47
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17722.46
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.35
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.56
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.82
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.46
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.34
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.42
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.49
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.73
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.64
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.96
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.67
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.65
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.75
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.72
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.42
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.65
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.64
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.72
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.06
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.20
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.00
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.27
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.39
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.85
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.43
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.62
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.21
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.32
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    2.13
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.13
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.99
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.09
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
 p-value of test no 205                :    0.9986
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.33
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.52
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9782.96
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 220                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.75
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.69
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.34
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.24
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.56
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.30
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.09
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000010498
 
 Normal statistic for number of bits   :   0.083
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.46
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000009088
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:52.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88703004.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56147
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7532
 p-value of test no 18                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.14
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.86
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.91
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.04
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.67
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.57
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.30
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.49
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.10
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7153.56
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.16
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.98
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.05
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.83
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908632
   j =  2                              :            45684
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908662
   j =  2                              :            45663
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.09
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.34
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.25
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.25
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.82
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.22
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.25
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.74
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.53
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.21
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.83
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.76
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.99
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.38
 p-value of test no 150                :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.48
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.91
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.08
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.53
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.50
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.91
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.60
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.76
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.41
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.12
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.45
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.54
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.11
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.80
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.68
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5232.60
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.61
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.77
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.88
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.51
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.50
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.66
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.68
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 187                :    0.9962
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.67
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   44.00
 p-value of test no 197                :  2.8e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.41
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.96
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.00
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.15
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.05
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.43
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.23
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.01
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.74
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.58
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.24
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.65
 p-value of test no 231                :  8.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000017668
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.63
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000061222
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:09.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  86  LongestHeadRun, r = 0           2.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89718812.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56148
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.96
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.53
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.03
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.79
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.52
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.97
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1290.94
 p-value of test no 56                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.42
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.73
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.55
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.87
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.28
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4844.08
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907658
   j =  2                              :            46168
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46259
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870259
   j =  1                              :        399907488
   j =  2                              :            46247
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
 p-value of test no 98                 :    0.9985
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.90
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.19
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.73
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.27
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.82
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.83
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.90
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.63
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.82
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.04
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.64
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.88
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.24
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   15.94
 p-value of test no 151                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.06
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.07
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.87
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.09
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.52
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.28
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.18
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.62
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.67
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.39
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.40
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.47
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.84
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.87
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.83
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.97
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.93
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.67
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.54
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.69
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.44
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.91
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.68
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.05
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.30
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.16
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.23
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.48
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.63
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.39
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.90
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.81
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.54
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.96
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.12
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.94
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.90
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.66
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.83
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999926993
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.02
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000103750
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    2.56
 p-value of test no 249                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:12.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90734620.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56149
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.70
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.61
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.76
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.58
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.04
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.97
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.52
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.26
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.93
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.09
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.01
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.17
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.31
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.71
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908261
   j =  2                              :            45859
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908485
   j =  2                              :            45747
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.35
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.00
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.65
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.75
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.10
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.59
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.25
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.65
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.88
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.37
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17650.13
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.04
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.84
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.75
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.38
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.64
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.00
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.87
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.69
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.06
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.16
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.28
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.19
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.04
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.91
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.35
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.13
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.56
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.97
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.49
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.65
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.50
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.62
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.23
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.62
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.60
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.11
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.92
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.18
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.44
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.20
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 186                :    0.9971
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.58
 p-value of test no 198                :  3.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 200                :  7.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.62
 p-value of test no 203                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 206                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.34
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.20
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.88
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.91
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.48
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.74
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.16
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.08
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.92
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.04
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999866024
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.58
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999952697
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:24.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91750428.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56150
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5609
 p-value of test no 13                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.00
 p-value of test no 46                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.36
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.37
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.49
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.06
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.06
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.59
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.30
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.55
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.94
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.87
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.06
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5172.46
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908277
   j =  2                              :            45854
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908598
   j =  2                              :            45698
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   35.09
 p-value of test no 120                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.24
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.99
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.64
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.56
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 126                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.75
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 130                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.45
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.68
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.69
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.66
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.85
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.89
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.03
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.64
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.37
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.16
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.34
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.28
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.76
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.72
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.86
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.53
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.97
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.67
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.43
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.02
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.01
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.34
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.91
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.74
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.31
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.35
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.70
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.72
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.27
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.98
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.60
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.55
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.58
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.66
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.46
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.04
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.09
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.61
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.51
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.45
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4349.95
 p-value of test no 227                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4282.92
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.11
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.12
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.88
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999947189
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.08
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000042472
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 237                :  6.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.59
 p-value of test no 238                :  4.8e-3
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:15.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92766236.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56151
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 7                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.15
 p-value of test no 40                 :  8.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.88
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.56
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.77
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.91
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.84
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.97
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  535.49
 p-value of test no 55                 :  6.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.57
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.09
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.20
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.59
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.94
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.42
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.14
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908553
   j =  2                              :            45719
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908149
   j =  2                              :            45921
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.91
 p-value of test no 116                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.70
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.03
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.08
 p-value of test no 121                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.52
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.28
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.84
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.09
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.30
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.93
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.68
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.35
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.99
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.46
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.08
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.68
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.50
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.20
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.31
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.61
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.70
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.24
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.77
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.76
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.57
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.91
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.98
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.80
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.12
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.26
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.91
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.77
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.01
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.39
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.38
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.71
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.88
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.20
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.63
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.98
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 186                :  1.2e-3
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.21
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.93
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.78
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.59
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.31
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.81
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.55
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.60
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.52
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.59
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.00
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000031477
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.95
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999944966
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:29.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  35  Gap, r = 25                     6.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93782044.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56152
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 3                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.93
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    3.02
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.81
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.18
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.29
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.07
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.99
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.95
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.60
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.86
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7449.17
 p-value of test no 57                 :  4.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.83
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.94
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.38
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.48
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908235
   j =  2                              :            45875
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907731
   j =  2                              :            46124
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-4
 p-value of test no 73                 :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9923
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.75
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.32
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.64
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.38
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.48
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.53
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.32
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.42
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.28
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17105.94
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.13
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.59
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.27
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.83
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.78
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.55
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.02
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.31
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.91
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.93
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.79
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.83
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.31
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.88
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.40
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.25
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.72
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.02
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.89
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.64
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.33
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.12
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.97
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.71
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.49
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.05
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.44
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.25
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.48
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.32
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.44
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.26
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.34
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.34
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.12
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.51
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.05
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.43
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.86
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.32
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.32
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.31
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000077080
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.00
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999948872
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:10.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  37  Gap, r = 20                     4.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94797852.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56153
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    3.15
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.24
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.99
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.11
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.86
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.32
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.03
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.28
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.25
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.23
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.03
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.63
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.05
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907927
   j =  2                              :            46029
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908555
   j =  2                              :            45718
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.00
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.22
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.85
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.79
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.79
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.53
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.91
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.86
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.73
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.84
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.72
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.83
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.82
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.98
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.61
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.36
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.42
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.21
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.03
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.91
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.15
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.98
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.13
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.71
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.39
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.62
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.05
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.00
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.82
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.31
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.39
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.75
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.95
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.75
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.76
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.82
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.66
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.81
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5262.09
 p-value of test no 173                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.02
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.49
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.62
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.35
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.05
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.16
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.05
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.44
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.93
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.19
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.05
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.10
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.88
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.12
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.47
 p-value of test no 231                :  7.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999859376
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.24
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000038194
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 235                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:44.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95813660.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56154
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 7                  :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7108
 p-value of test no 20                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 29                 :    0.9939
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.02
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.33
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.21
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.39
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.69
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.40
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.64
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.38
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.45
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.28
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.21
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.22
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.47
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.17
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.23
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.35
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907956
   j =  2                              :            46019
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46408
 p-value of test no 71                 :  6.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870408
   j =  1                              :        399907189
   j =  2                              :            46398
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 94                 :    0.9935
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 114                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.77
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.03
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.68
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.74
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.43
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.33
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.75
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.82
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.26
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.39
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.08
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.19
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.59
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.80
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.42
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.11
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.60
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.50
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.22
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.95
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.56
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.91
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.69
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.04
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.27
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.30
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.42
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.51
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.89
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.82
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.22
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.05
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4793.80
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.50
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.42
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.41
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.92
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.26
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.17
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.40
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.25
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.14
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.46
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.88
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.51
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.57
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.48
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.69
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000142735
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.57
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999826637
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:34.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            8.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96829468.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56155
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     543
 p-value of test no 31                 :    0.9903
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.17
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.00
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.87
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.98
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.28
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.66
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.03
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.12
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.24
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.67
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.27
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.23
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.01
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45701
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908600
   j =  2                              :            45697
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908256
   j =  2                              :            45866
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 80                 :    0.9920
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.08
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.98
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.90
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.87
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.86
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.31
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.65
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.80
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.30
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.40
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.71
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.30
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.86
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.80
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.36
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.90
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.80
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.94
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.82
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.95
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.32
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.98
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.27
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.36
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.47
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.27
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.18
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.55
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.41
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.19
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.71
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.55
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.03
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.29
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.23
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.01
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.27
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.90
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.35
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.70
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.39
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.38
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.05
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.09
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.53
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.10
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.00
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.76
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000018148
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.20
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999961310
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:50.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97845276.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56156
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.02
 p-value of test no 28                 :  8.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    3.32
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.75
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.18
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.07
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.01
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.18
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.85
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.76
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.05
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.91
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.11
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.18
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.98
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45600
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908804
   j =  2                              :            45592
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45584
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908836
   j =  2                              :            45576
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 104                :  9.0e-4    *****
 
 Anderson-Darling statistic = A2       :    4.85
 p-value of test no 105                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.95
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.40
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.30
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.51
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.07
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.91
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.08
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.14
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.48
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17611.11
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.25
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.23
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.15
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.20
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.34
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.90
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.98
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.60
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.27
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.35
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.77
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.68
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.56
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.75
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.43
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.02
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.90
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.11
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.00
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.21
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.17
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.88
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.84
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.65
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.91
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.41
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.71
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.99
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.99
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.18
 p-value of test no 184                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.38
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.14
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.66
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.42
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.88
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.86
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.15
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.73
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4295.47
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.80
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11552.85
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.09
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000076882
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.50
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999990278
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:49.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98861084.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56157
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4171
 p-value of test no 17                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.21
 p-value of test no 23                 :  7.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9929
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.91
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.56
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.31
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.45
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.15
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6811.65
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.95
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 64                 :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.28
 p-value of test no 65                 :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.96
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.93
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4854.72
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45582
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869582
   j =  1                              :        399908840
   j =  2                              :            45574
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45479
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869479
   j =  1                              :        399909048
   j =  2                              :            45467
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-4
 p-value of test no 109                :  2.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-6
 p-value of test no 110                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    5.40
 p-value of test no 111                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.75
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.63
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.08
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.60
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.76
 p-value of test no 124                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.49
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.13
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.63
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.93
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 142                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17757.06
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.92
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.42
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.14
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.35
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.47
 p-value of test no 150                :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.75
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.35
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.09
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.70
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.59
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.35
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.22
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.86
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.83
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.20
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.93
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.84
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.60
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.40
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.31
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.61
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.13
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.91
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.06
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.81
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.88
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.62
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.64
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.45
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.51
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.23
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.56
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.99
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.49
 p-value of test no 207                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.65
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.24
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.12
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.56
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.15
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.74
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.69
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.28
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.83
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000012346
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.01
 p-value of test no 233                :    0.9967
 
 
 -----------------------------------------------
 Total number of bits:  7999930971
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.077
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:18.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99876892.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56158
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.90
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.96
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.00
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.62
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.12
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.32
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.27
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7267.43
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.00
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.45
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.45
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.19
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.67
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46361
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870361
   j =  1                              :        399907283
   j =  2                              :            46351
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908371
   j =  2                              :            45810
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.42
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.23
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.08
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.02
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.64
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.95
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.74
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9921
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.84
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.12
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.46
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.55
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.54
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.48
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.76
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.72
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.15
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.28
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.54
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.26
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.72
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.15
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.61
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.26
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.27
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.80
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.04
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.82
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.44
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.94
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.41
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.37
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.37
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.52
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.98
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.73
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.70
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.59
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.23
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.67
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.71
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.20
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.86
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.23
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.13
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.05
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10237.46
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.88
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.85
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.20
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.81
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.89
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.05
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.32
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999966908
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.18
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000130537
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:39.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100892700.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56159
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 12                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.03
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.72
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.91
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.77
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.93
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.83
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.55
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.22
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.98
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.04
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.79
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.20
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.38
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.20
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908373
   j =  2                              :            45803
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908537
   j =  2                              :            45730
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.91
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.64
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.38
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.18
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.29
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.26
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.06
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.17
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.87
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.70
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.65
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.88
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.70
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.14
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.88
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.01
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.87
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.83
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.55
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.77
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.12
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.70
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.80
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.67
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.93
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.35
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.42
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.15
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.10
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.23
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.17
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.03
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.36
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.40
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.63
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.16
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.49
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.70
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.19
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10157.73
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.03
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.03
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.30
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4295.54
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.01
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.69
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.74
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.49
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000016654
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.71
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000023719
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:02.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101908508.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56160
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    3.00
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.16
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.55
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.39
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.48
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.49
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.68
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.47
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.65
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1315.87
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7225.22
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.06
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.80
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.84
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.91
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907859
   j =  2                              :            46063
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908378
   j =  2                              :            45805
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.76
 p-value of test no 118                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.90
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.78
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.96
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.30
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.66
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.07
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.50
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.85
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.29
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.14
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.83
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    6.89
 p-value of test no 149                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.46
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.56
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.95
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.71
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.82
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.83
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.15
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.09
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.74
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.64
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.01
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.12
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.12
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.03
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.74
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.93
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.99
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.39
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.77
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.61
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.03
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.70
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.22
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.64
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.99
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.15
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.96
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.92
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.30
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10282.55
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.37
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.74
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.94
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.92
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.06
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.03
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.91
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.64
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999880955
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.50
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999978296
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:28.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 R (L=50, r=0)       0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83525661.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56161
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     522
 p-value of test no 31                 :    0.9994    *****
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.66
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    3.51
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.00
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.59
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.37
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.59
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7229.98
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.42
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.48
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.49
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.69
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.90
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907755
   j =  2                              :            46121
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908579
   j =  2                              :            45700
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.78
 p-value of test no 119                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.80
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.08
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.07
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.04
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.54
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.41
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.50
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.91
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17672.25
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.72
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.04
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.73
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.95
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.69
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.96
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.77
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.56
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.06
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.79
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.61
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.29
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.26
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.48
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.90
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.82
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.92
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.45
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.44
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.06
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.99
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.36
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.75
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.72
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.20
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.72
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.61
 p-value of test no 176                :  6.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.17
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    2.05
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.77
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.77
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.25
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.53
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.53
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.09
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.82
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.50
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.60
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.90
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.14
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999906590
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.12
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000025939
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:42.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        0.9994 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84541469.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56162
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7550
 p-value of test no 21                 :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    4.25
 p-value of test no 39                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.27
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.77
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.01
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.34
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.46
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.10
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  513.74
 p-value of test no 55                 :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.61
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6855.24
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.49
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.43
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.26
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.49
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.64
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45453
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869453
   j =  1                              :        399909096
   j =  2                              :            45449
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.41
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.78
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.04
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.83
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.82
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.21
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.05
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.91
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.57
 p-value of test no 146                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.05
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.60
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.28
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.27
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.98
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.79
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.84
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.53
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.49
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.01
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.30
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.04
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.88
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.25
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.68
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.98
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.94
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.13
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.56
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.43
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.99
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.42
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.92
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.63
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.62
 p-value of test no 172                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.31
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.51
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.43
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.53
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.69
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.79
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.64
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.20
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.07
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.44
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.58
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.91
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.20
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.43
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.22
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000037561
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.65
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999908447
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:05.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85491741.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56163
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.56
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.83
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.09
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.92
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.14
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.14
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.56
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.49
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.11
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.43
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.43
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.84
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.54
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908198
   j =  2                              :            45892
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907947
   j =  2                              :            46022
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9904
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.56
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.80
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.33
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.93
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.67
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.22
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.73
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.36
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.76
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17157.51
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.07
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.98
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.14
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.08
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.75
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.12
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.25
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.73
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.36
 p-value of test no 156                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.91
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.12
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.06
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.50
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.72
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.88
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.34
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.84
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.58
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.82
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.79
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.82
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.31
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.77
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.34
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.66
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.16
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.99
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.92
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.17
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.69
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.18
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 214                :  9.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9629.59
 p-value of test no 215                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.95
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.24
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.10
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.65
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.14
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.11
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.85
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000121816
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.39
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000128131
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:29.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86507549.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56164
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 11                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.39
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.96
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.71
 p-value of test no 50                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.29
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.03
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.03
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.84
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.48
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1331.54
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.96
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.51
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.62
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.36
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.31
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4908.91
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908409
   j =  2                              :            45791
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908458
   j =  2                              :            45765
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 91                 :    0.9918
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.84
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.00
 p-value of test no 120                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.58
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.47
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.27
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.34
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.73
 p-value of test no 129                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.17
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.02
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17690.56
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.78
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.30
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.75
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.87
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.18
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.22
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.19
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.25
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.32
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.25
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.56
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.87
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.97
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.06
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.26
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.41
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.13
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.15
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.60
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.66
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.60
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.69
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.72
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.40
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.11
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.41
 p-value of test no 178                :    0.9919
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 200                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.50
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.82
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.94
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.94
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.24
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.58
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4330.34
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.36
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12081.30
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.84
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.53
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000084694
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.28
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000031459
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:35.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87392285.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56165
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 4                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.55
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.88
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.53
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.17
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.44
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.60
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.86
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.00
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.56
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.40
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.45
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.10
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.15
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   21.66
 p-value of test no 66                 :  6.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.18
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.59
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908384
   j =  2                              :            45802
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908682
   j =  2                              :            45653
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.30
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.06
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.16
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.34
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.42
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.39
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.97
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 132                :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.21
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.07
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.86
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.17
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.98
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.48
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.85
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.69
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.85
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.00
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.14
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.02
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.53
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.15
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.87
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.31
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.64
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.24
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.21
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.75
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.03
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.34
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.57
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.10
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.87
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.99
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.03
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.65
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.89
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.81
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.18
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.30
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.52
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.55
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.31
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.55
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.79
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.62
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.32
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.58
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.63
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.32
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.38
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000104146
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.41
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000018412
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:07.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              6.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88375325.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56166
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 7                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.70
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9900
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.27
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 39                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.41
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.89
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.98
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.68
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.39
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.78
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1553.53
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.81
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.98
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.21
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.43
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.07
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46324
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870324
   j =  1                              :        399907356
   j =  2                              :            46316
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907862
   j =  2                              :            46063
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.4e-3
 
 Anderson-Darling statistic = A2       :    5.88
 p-value of test no 81                 :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  1.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
 p-value of test no 86                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.9e-3
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.96
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.38
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.29
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.90
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.66
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.22
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.68
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.18
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.81
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.86
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.70
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.26
 p-value of test no 149                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.81
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.30
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.33
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.16
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.70
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.33
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.91
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.56
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.45
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.87
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.41
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.15
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.65
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.72
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.94
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.46
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.79
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.89
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.22
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.64
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.82
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.80
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.96
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.52
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.59
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.53
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.53
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.40
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.63
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.96
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.71
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.25
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.59
 p-value of test no 217                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.80
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.45
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.92
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.41
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.75
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.06
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.67
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999994373
 
 Normal statistic for number of bits   :  -0.044
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.45
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999864452
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:31.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89423901.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56167
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1247
 p-value of test no 10                 :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334367
   j =  1                              :        599997506
   j =  2                              :             1247
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.67
 p-value of test no 23                 :  4.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9908
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.32
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.88
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.33
 p-value of test no 50                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.13
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.12
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.38
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.85
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.29
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.86
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.77
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.70
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.63
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.84
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908056
   j =  2                              :            45972
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908255
   j =  2                              :            45868
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.99
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.41
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.54
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.82
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.22
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.30
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.71
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.76
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.04
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.71
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.36
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.33
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.81
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.45
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.15
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.91
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.82
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.64
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.72
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.24
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.37
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.34
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.60
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.34
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.17
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.80
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.74
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.87
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.15
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.16
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.83
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.32
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.78
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.35
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.20
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.57
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.22
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.02
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.39
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.91
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.40
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.07
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.14
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.81
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.51
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.63
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.03
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.78
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.05
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.85
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.62
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.40
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.45
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.64
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999784037
 
 Normal statistic for number of bits   :   -1.71
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.99
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999978179
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:17.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90439709.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56168
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.13
 p-value of test no 32                 :    0.9994    *****
 
 Stat. AD after spacings (mNP2-S)      :    4.53
 p-value of test no 33                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   51.01
 p-value of test no 48                 :  5.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.93
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.98
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.92
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.02
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.62
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.94
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.50
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.43
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.24
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.07
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.94
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.34
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.38
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908118
   j =  2                              :            45938
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908661
   j =  2                              :            45665
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 103                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.64
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.70
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.10
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.62
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.26
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.68
 p-value of test no 124                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.89
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.94
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.05
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.039
 p-value of test no 135                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.38
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17666.05
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.41
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.66
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.73
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.84
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.44
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.04
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.76
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.20
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.41
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.76
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  608.23
 p-value of test no 158                :  6.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.62
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.57
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.94
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.19
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.07
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.62
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.38
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.42
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.11
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.79
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.61
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.61
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.72
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.72
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.90
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.56
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.99
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.36
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.99
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.63
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.80
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.49
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.55
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.58
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.69
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.09
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.23
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.67
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12057.46
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.15
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.71
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999754487
 
 Normal statistic for number of bits   :   -1.94
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.43
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999911435
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:40.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          0.9994 
  28  SimpPoker, r = 0                5.3e-5
  76  RandomWalk1 J (L=1000, r=0)     6.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91389981.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56169
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9907
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.63
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.47
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.61
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.36
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.02
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.91
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.50
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.17
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.19
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.53
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.39
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.72
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908293
   j =  2                              :            45852
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908029
   j =  2                              :            45978
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.20
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.45
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.99
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.12
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.24
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.21
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.66
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.04
 p-value of test no 129                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.31
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.96
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.03
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.03
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.50
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.66
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.09
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.14
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.95
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.20
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.08
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.63
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.01
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.36
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.53
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.38
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.71
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.25
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.28
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.20
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.93
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.80
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.26
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.79
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.29
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.58
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.74
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.45
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.72
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.56
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.72
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.90
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.58
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.85
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.31
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9967
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.43
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.00
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.80
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.35
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.52
 p-value of test no 218                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.56
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.88
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.75
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.29
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.40
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11632.50
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.00
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999943112
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.96
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000018760
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:05.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92536861.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56170
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.53
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.72
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.71
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.58
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.95
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.36
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.45
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.80
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.59
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.13
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.44
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.55
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.23
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.06
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908106
   j =  2                              :            45941
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.04
 p-value of test no 117                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.03
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.75
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.89
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.58
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.26
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.08
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.70
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.29
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.55
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.09
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.98
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.40
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.21
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.69
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.44
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.92
 p-value of test no 151                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.70
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.65
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.34
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.80
 p-value of test no 156                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.60
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.41
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.26
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.70
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.73
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.87
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.40
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.67
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.62
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.02
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.83
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.95
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.56
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.15
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.27
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.89
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.05
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.23
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.03
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.17
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 195                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.47
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.08
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.58
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.87
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 221                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5170.56
 p-value of test no 222                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.01
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.79
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.79
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.60
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.87
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.22
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000059275
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.67
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000103258
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:57.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  85  Fourier3, r = 27                0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93552669.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56171
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    4.53
 p-value of test no 27                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.25
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.80
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.46
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.67
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.61
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.60
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.48
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.22
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.67
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.37
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.96
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.55
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  8.2e-3
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 64                 :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.36
 p-value of test no 65                 :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.27
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4870.41
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908142
   j =  2                              :            45923
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908303
   j =  2                              :            45841
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  6.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 78                 :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.89
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.74
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.95
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.49
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.28
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.08
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.64
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.24
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.89
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.72
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.17
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.20
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.60
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.49
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.58
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.74
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.70
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.22
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.49
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.11
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.55
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.96
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.02
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.53
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.69
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.90
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.47
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.77
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4797.45
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.32
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.69
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.05
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.86
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.33
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.26
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.25
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.29
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.08
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.32
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 210                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.62
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.62
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.39
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.06
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.31
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3939.89
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.35
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.39
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.59
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999898571
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.77
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000018163
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    2.05
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:00.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94634013.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56172
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 9                  :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4188
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.67
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.00
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.70
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.74
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.48
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.18
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.13
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.92
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.76
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.64
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.16
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.53
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908484
   j =  2                              :            45755
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46349
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870349
   j =  1                              :        399907305
   j =  2                              :            46343
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.24
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.88
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.60
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.64
 p-value of test no 123                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.71
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.41
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.81
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.80
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17674.91
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.44
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.18
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.29
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.98
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.86
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.73
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.78
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.72
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.45
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.19
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.03
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.65
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.64
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.63
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.07
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.38
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.88
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.09
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.69
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.85
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.78
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.42
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.03
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.40
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.88
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.09
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.86
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.39
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.72
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.72
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.44
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.04
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.29
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.97
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.03
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11543.17
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.03
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000046426
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.83
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999998819
 
 Normal statistic for number of bits   : -9.34e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:12.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95584285.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56173
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.23
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.17
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.59
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.64
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.52
 p-value of test no 51                 :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.15
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.49
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.67
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.76
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.06
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.52
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.92
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.86
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.52
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.99
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46294
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907413
   j =  2                              :            46292
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908160
   j =  2                              :            45914
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.14
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.34
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.82
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.08
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.35
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.32
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.38
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.15
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.00
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17409.65
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.93
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.85
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.30
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.40
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.64
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.92
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.37
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.84
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.30
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.53
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.53
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.72
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.42
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.86
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.45
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.46
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.19
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.50
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.34
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.82
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.19
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.87
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.41
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.44
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.95
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.25
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.11
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.00
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.46
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.67
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.47
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.09
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.06
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.29
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.81
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.00
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.57
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.95
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.07
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999921497
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.02
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000156508
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:48.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96501789.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56174
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.41
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.66
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.45
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.44
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.95
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.84
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.94
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.69
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.46
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.79
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.96
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4862.20
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46521
 p-value of test no 70                 :  1.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870521
   j =  1                              :        399906964
   j =  2                              :            46509
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908487
   j =  2                              :            45752
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.03
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.20
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.35
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.26
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.36
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.99
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.28
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.00
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.56
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.45
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.13
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.72
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.64
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.36
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.30
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.77
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.99
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.82
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.16
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.94
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.11
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.39
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.15
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.05
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.40
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.52
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.01
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.75
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.01
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.77
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  142.06
 p-value of test no 170                :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.50
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.57
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.47
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.74
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.67
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.65
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.47
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.26
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.60
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.93
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.21
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.14
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.53
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.22
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.02
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.89
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.78
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.95
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999720350
 
 Normal statistic for number of bits   :   -2.21
 p-value of test no 232                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.67
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999988694
 
 Normal statistic for number of bits   :  -0.089
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
 p-value of test no 251                :    0.9962
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:46.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 C (L=10000, r=0)    0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97353757.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56175
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 12                 :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    3.95
 p-value of test no 33                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9924
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.08
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.70
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.28
 p-value of test no 52                 :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.49
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.48
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.49
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7156.78
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.28
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.58
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.93
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.16
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46140
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907722
   j =  2                              :            46136
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907648
   j =  2                              :            46173
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.23
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.08
 p-value of test no 120                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.15
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.35
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.15
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.49
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.74
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.48
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.12
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.17
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.37
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.81
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.69
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.50
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.85
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.73
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.57
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.91
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.86
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.69
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.87
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.49
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.34
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.27
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.37
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.22
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.89
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.88
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.95
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.16
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.80
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.00
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.09
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.85
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5218.40
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.36
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.04
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.18
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.28
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 180                :  3.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    5.28
 p-value of test no 182                :  2.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.77
 p-value of test no 183                :    0.9972
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.19
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.32
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.61
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.75
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10174.94
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.90
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.22
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.80
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.87
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.96
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.13
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.12
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000010063
 
 Normal statistic for number of bits   :   0.080
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.73
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999852530
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 247                :  4.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.88
 p-value of test no 248                :    0.9980
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:27.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98467869.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56176
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.64
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.74
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.56
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.65
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.71
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.31
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.98
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.49
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.89
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.96
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6813.43
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.66
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
 p-value of test no 63                 :    0.9973
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.34
 p-value of test no 65                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.37
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.80
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908258
   j =  2                              :            45865
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908353
   j =  2                              :            45819
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.00
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.66
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.66
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.28
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.90
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.22
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.96
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.01
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17068.40
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.27
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.75
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.72
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.14
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.73
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.66
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.97
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.65
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.32
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.19
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.63
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.71
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.01
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.56
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.76
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.06
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.52
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.31
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.15
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.74
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.47
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.87
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.08
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.18
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.17
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.26
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.34
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.48
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.18
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.33
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.52
 p-value of test no 178                :    0.9981
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.04
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.56
 p-value of test no 198                :    0.9917
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.27
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.62
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.57
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.54
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.86
 p-value of test no 218                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.37
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.05
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.06
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.76
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.91
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.18
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.94
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000088297
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.21
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000113239
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:27.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99549213.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56177
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.07
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.19
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.97
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.64
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.88
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.48
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.21
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.25
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.84
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6747.09
 p-value of test no 57                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.10
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.64
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.68
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.09
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.15
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907860
   j =  2                              :            46064
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908235
   j =  2                              :            45875
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.02
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.05
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.06
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.19
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.98
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 131                :    0.9937
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.63
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.10
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 142                :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17048.55
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.38
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.56
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.84
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.97
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.65
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.21
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.40
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.74
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.61
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.78
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.98
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.99
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.34
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.68
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.78
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.57
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.16
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.32
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.69
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.63
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.56
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.90
 p-value of test no 169                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.78
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.17
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.19
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.38
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.81
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.46
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.96
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 188                :    0.02
 
 Sample variance                       :    2.17
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.40
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.49
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.75
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.62
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.76
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.44
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.78
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.48
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.68
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.71
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.12
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999937547
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.15
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999996491
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:11.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100433949.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56178
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.92
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.26
 p-value of test no 40                 :  2.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.94
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.96
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.98
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.87
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.92
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.86
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.51
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.90
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.81
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.50
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.86
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.82
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.72
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.02
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.29
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908001
   j =  2                              :            45998
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 74                 :    0.9960
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.33
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.90
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.65
 p-value of test no 123                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.30
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.65
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.49
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.32
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.80
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.39
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.87
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.26
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.78
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.80
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.48
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.41
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.76
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.05
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.22
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.26
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.01
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.50
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.45
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.50
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.86
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.64
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.23
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.28
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.90
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.00
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.14
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.21
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.38
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.05
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.10
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.07
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.36
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.86
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.83
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.93
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.34
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.84
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.34
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.10
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.76
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.34
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.66
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.93
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.47
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.79
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.21
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000033430
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.80
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999886796
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:42.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101318685.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56179
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.12
 p-value of test no 40                 :  8.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.06
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.09
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.99
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.24
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.15
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.44
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.57
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.43
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.15
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.44
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.12
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.12
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.05
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.43
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908024
   j =  2                              :            45985
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908204
   j =  2                              :            45892
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
 p-value of test no 77                 :    0.9974
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
 p-value of test no 87                 :    0.9982
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.96e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.10
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.78
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.37
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.85
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.06
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.51
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.45
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.09
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.59
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.78
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.94
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.99
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.41
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.14
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.98
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.24
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.05
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.49
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.80
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.24
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.75
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.78
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.88
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.45
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.04
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.29
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.91
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.35
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.11
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.59
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.72
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.50
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.54
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.70
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.54
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.60
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.23
 p-value of test no 196                :    0.9964
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.55
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.32
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.07
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.89
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.82
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.74
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3900.28
 p-value of test no 227                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.01
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.81
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12159.03
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.13
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999926840
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.19
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000212875
 
 Normal statistic for number of bits   :    1.68
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:29.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102301725.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56180
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    2.58
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.39
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.71
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.31
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.44
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.19
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.22
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.27
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.65
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7305.24
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.13
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.57
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.74
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.14
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.79
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908214
   j =  2                              :            45890
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908537
   j =  2                              :            45730
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.43
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.55
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.14
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.56
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.71
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.83
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.82
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.93
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.98
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17610.88
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.73
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.91
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.47
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.94
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.83
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.51
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.71
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.09
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.72
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.59
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.81
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.47
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.22
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.89
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.31
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  112.33
 p-value of test no 165                :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.49
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.78
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.24
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.96
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.72
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.93
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.32
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.68
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.81
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.56
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.15
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.82
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.96
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10235.24
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.95
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.34
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.87
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.84
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.98
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.00
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.25
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999887678
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.89
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000122950
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9918
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:56.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83558430.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56181
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 11                 :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.38
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.65
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.26
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.21
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.33
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.93
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.92
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.65
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.78
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.45
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.52
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.24
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.37
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.74
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.25
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.51
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908535
   j =  2                              :            45728
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45557
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869557
   j =  1                              :        399908889
   j =  2                              :            45551
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.27
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.10
 p-value of test no 120                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.92
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.03
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.29
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.52
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.65
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.42
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.54
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.22
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.57
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.00
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.68
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.03
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.24
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.67
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.39
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.72
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.08
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.76
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.65
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.79
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.45
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.49
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.28
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.54
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.97
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.89
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.63
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.54
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.35
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.06
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.84
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.80
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.46
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.95
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.29
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.59
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.17
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.82
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.37
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.87
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.30
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.04
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.78
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3922.74
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.50
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11359.69
 p-value of test no 229                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.46
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.20
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000073852
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.77
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999997106
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:46.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83591198.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56182
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4181
 p-value of test no 17                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.45
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.99
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.79
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.18
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.57
 p-value of test no 52                 :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.78
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.58
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.91
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.66
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.27
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.47
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.60
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.59
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.73
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.48
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908239
   j =  2                              :            45876
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907912
   j =  2                              :            46041
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
 p-value of test no 79                 :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.81
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.40
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.28
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.26
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.01
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.34
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.52
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17715.24
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.25
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.85
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.69
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.70
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.03
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.63
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.21
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.56
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.36
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.22
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.35
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.94
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.95
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.69
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.47
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.57
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.63
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.49
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.32
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.01
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.26
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.54
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.82
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.46
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.60
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.81
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.17
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.64
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.59
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.87
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.62
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.57
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.22
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.87
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.94
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.85
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.81
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.64
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000140752
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.96
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000074782
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:51.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84607006.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56183
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.00
 p-value of test no 46                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.19
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.50
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.71
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.39
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.11
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.57
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.27
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.36
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.81
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.33
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.85
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908083
   j =  2                              :            45954
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907932
   j =  2                              :            46031
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.91
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.95
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.60
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.23
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.63
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.35
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.28
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.26
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.71
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.58
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.55
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.63
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.20
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.47
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.84
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.70
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.62
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.01
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.07
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.38
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.34
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.57
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.50
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.90
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.46
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.81
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.27
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.10
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.37
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.17
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.47
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.93
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.39
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.87
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.25
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.93
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.56
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.70
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.39
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.61
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.40
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.97
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.87
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.13
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.75
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.99
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.80
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.50
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   25.58
 p-value of test no 231                :    0.9996    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000061600
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.65
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000027598
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:05.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  101  Run of bits, r = 0              0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85622814.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56184
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4158
 p-value of test no 14                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.30
 p-value of test no 28                 :  6.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.81
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.85
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.84
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.99
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.68
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.86
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.18
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.69
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.90
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.18
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.40
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.29
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.63
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.79
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908397
   j =  2                              :            45797
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908362
   j =  2                              :            45819
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.93
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.57
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.02
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.12
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.13
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.95
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.57
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.34
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.17
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.31
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.77
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.92
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.77
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.47
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.80
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.56
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.88
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.09
 p-value of test no 152                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.44
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.64
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.88
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.79
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.38
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.47
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.74
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.13
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.30
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.20
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.17
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.31
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.37
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.04
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.96
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.62
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.02
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.98
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.68
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.43
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.83
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.11
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    2.18
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.02
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.95
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.37
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.25
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 218                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.96
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.03
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.50
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.37
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.11
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.87
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.17
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999900845
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.55
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999961517
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:43.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86638622.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56185
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    5.27
 p-value of test no 27                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.21
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.66
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.44
 p-value of test no 50                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.67
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.60
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.73
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.85
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.88
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.71
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.12
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.64
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.30
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.89
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.28
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.94
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907840
   j =  2                              :            46080
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908544
   j =  2                              :            45728
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-4
 p-value of test no 110                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    5.06
 p-value of test no 111                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.16
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.50
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.52
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.73
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.98
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.95
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.02
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.00
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17719.10
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.86
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.88
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.57
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.94
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.87
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.32
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.43
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.68
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.66
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.59
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.02
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.77
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.85
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.97
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.30
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.26
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.88
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.84
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.26
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.78
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.28
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.71
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.74
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.78
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.71
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.91
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.46
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.62
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 190                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.17
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.22
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.41
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.53
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9784.29
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.51
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.63
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.19
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3955.47
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.13
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.87
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.95
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999885053
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.02
 p-value of test no 233                :  1.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000215701
 
 Normal statistic for number of bits   :    1.71
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 251                :    0.9936
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 252                :  8.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.76
 p-value of test no 253                :    0.9971
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:17.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87654430.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56186
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.50
 p-value of test no 23                 :  5.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.47
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.82
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.25
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.06
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.61
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.35
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.92
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.73
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.44
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.29
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.10
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.93
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.87
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45494
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869494
   j =  1                              :        399909015
   j =  2                              :            45488
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45341
 p-value of test no 71                 :    0.9941
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869341
   j =  1                              :        399909323
   j =  2                              :            45331
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 73                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 74                 :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  9.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.16
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.78
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.50
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.70
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.97
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.32
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.40
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.92
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17642.09
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.16
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.43
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.23
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.60
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.60
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.08
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.18
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.87
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.30
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.30
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.50
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.66
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.14
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.69
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.63
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.67
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.32
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.61
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.65
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.47
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.53
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.23
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.77
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  296.39
 p-value of test no 172                :    0.9997    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.22
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.02
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.71
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.81
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.48
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.27
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.33
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.35
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.70
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.91
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.73
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.55
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.05
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.41
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.24
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000083620
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.78
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000106546
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :   0.081
 p-value of test no 239                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 240                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:18.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88670238.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56187
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5231
 p-value of test no 13                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7094
 p-value of test no 15                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    5.69
 p-value of test no 33                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    3.64
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.34
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.55
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.47
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.32
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.70
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.09
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.58
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.77
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.37
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.97
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.69
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.59
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.58
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.64
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908728
   j =  2                              :            45627
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908585
   j =  2                              :            45703
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.97
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.86
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.13
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.15
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.20
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.45
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.53
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.38
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17662.21
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.73
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.05
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.10
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.83
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.09
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.74
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.76
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.57
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.43
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.97
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.87
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.17
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.33
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.26
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.58
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.69
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.39
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.89
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.08
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.41
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.14
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.98
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.53
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.14
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.51
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.27
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.00
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.17
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.62
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.67
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.91
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.34
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.17
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.07
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.37
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.76
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.67
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.68
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.03
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999853607
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.29
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000125089
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:33.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89686046.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56188
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 3                  :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.52
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.46
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.89
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.74
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.34
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.41
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.96
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.85
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.76
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.61
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.09
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.17
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.73
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.63
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908761
   j =  2                              :            45609
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46306
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870306
   j =  1                              :        399907393
   j =  2                              :            46296
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.4e-3
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 85                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.37
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.11
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.37
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.53
 p-value of test no 125                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.09
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.18
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.21
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.40
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17614.11
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.96
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.57
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.07
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.21
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.45
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.62
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.79
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.08
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.22
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.85
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.30
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.96
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.95
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.20
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.98
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.42
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.34
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.58
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.08
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.94
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.50
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.19
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.32
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.95
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.56
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.24
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.77
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.69
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.04
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.59
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.52
 p-value of test no 178                :    0.9907
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-4
 p-value of test no 193                :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.12
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.05
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.41
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.46
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.00
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.72
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5098.51
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.04
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.47
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.28
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11329.67
 p-value of test no 229                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.74
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.61
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000170752
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.91
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999968351
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:31.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  99  HammingIndep, L=1200, r=0       0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90701854.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56189
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5613
 p-value of test no 13                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.55
 p-value of test no 22                 :  1.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.04
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.94
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.89
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.90
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.32
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.79
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  171.37
 p-value of test no 54                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.22
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.01
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.77
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.98
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.07
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.33
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.10
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.04
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907954
   j =  2                              :            46023
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45468
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869468
   j =  1                              :        399909070
   j =  2                              :            45456
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 92                 :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.29
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.58
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.03
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.37
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.70
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.31
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.25
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.61
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17841.58
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.09
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.95
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.07
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.63
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.06
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.97
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.97
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.77
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.53
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.08
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.06
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.46
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.99
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.77
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.62
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.34
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.35
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.24
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.07
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.18
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.11
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.37
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.46
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.49
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.15
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.91
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.90
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.93
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.68
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.59
 p-value of test no 176                :    0.9978
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.09
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.53
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.40
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.80
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.13
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.48
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.94
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.27
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.04
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.40
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.36
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.74
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000026527
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.24
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000177142
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:06.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91717662.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56190
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.15
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    3.59
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.02
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.25
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.53
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.18
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.55
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.55
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.44
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.84
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.75
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.04
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.52
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.39
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.12
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.97
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907813
   j =  2                              :            46089
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45603
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869603
   j =  1                              :        399908797
   j =  2                              :            45597
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 98                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-4
 p-value of test no 109                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.12
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.76
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.11
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.79
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.07
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.21
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.30
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.33
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.75
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.19
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.30
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.27
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.74
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.87
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.36
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.05
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.70
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.55
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.78
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.49
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.83
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.77
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.16
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.03
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.64
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.66
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.52
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.61
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.99
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.40
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.92
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.62
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.35
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.73
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.88
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.40
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.83
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.02
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.05
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.50
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.43
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.71
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.42
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.98
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.60
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.49
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.50
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.99
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.87
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.69
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.80
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000118744
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.59
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000111331
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.069
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:00.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92733470.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56191
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.08
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.03
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.79
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.61
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.25
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.28
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.42
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.90
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.90
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.60
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.48
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.76
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908275
   j =  2                              :            45855
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908152
   j =  2                              :            45915
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.59
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.49
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.55
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.20
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 126                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 127                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 128                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.53
 p-value of test no 129                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.40
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.93
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.16
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.63
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.85
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.67
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.87
 p-value of test no 149                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.66
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.99
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.87
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.61
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.04
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.10
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.15
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.04
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.06
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.02
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.45
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.05
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.38
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.34
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.43
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.89
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.41
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.00
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.93
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.18
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.00
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.13
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.44
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.84
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.38
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.71
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.32
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.12
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.49
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.93
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.58
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.56
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12143.88
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.49
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.79
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000077044
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.13
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999886346
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 238                :    0.47
 
 Sample variance                       :    2.20
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:23.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93749278.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56192
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4169
 p-value of test no 14                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.47
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.35
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.04
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.41
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.11
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.36
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.37
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.60
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.48
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.86
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7195.86
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 60                 :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.51
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.37
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.11
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.23
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.72
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45636
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908731
   j =  2                              :            45630
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907813
   j =  2                              :            46089
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.52
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.35
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.52
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.86
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.14
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.86
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.54
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.68
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.28
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.34
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.47
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.51
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.48
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.18
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.94
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.83
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.73
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.70
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.17
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.70
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.41
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.38
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.57
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.94
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.76
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.31
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.13
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.72
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.33
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.09
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.33
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.99
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.31
 p-value of test no 171                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.42
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4759.11
 p-value of test no 173                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.38
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.83
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.26
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 200                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.07
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.76
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.64
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.58
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.60
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.40
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.53
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.75
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.32
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.30
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.03
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000050515
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.29
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000023563
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.14
 p-value of test no 254                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:43.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94765086.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56193
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7555
 p-value of test no 15                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.65
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.10
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.32
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.28
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.44
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.64
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7189.79
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.28
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.60
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.97
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.25
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.00
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908295
   j =  2                              :            45845
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46278
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870278
   j =  1                              :        399907447
   j =  2                              :            46272
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.49
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.70
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.44
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.70
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.51
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.67
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.51
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.94
 p-value of test no 137                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.05
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.34
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.23
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.70
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.06
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.58
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.14
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.22
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.94
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.35
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.05
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.05
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.34
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.80
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.08
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.68
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.59
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.43
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.34
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.52
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.79
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.34
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.76
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.44
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.71
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.70
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.30
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.58
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    2.20
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.38
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.27
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.14
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.65
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.84
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.26
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.82
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.09
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.93
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.96
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.29
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.63
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999918323
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.26
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999863231
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9923
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 253                :    0.49
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:52.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95780894.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56194
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.16
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.09
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.82
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.44
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.11
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.90
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.41
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.94
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7297.80
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.11
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.31
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.42
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.64
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.88
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908515
   j =  2                              :            45738
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908756
   j =  2                              :            45619
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 108                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.89
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.67
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.10
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.90
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.59
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.29
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.41
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.50
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.34
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.07
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17688.08
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.96
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.40
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.49
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.72
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.55
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.60
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.16
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.36
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.79
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.42
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.86
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.17
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.78
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.13
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.85
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.73
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.32
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.79
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.29
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.76
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.93
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.23
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.60
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.56
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.63
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.04
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.96
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.61
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.02
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.38
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.91
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.45
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.45
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.025
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.72
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.65
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.88
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.77
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.13
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.25
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.02
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999882710
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.18
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000130327
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9967
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 1.40e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:26.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96796702.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56195
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 9                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.02
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.35
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.92
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.55
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.81
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.66
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.99
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.72
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.97
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.57
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.62
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.38
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5191.52
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908306
   j =  2                              :            45841
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907863
   j =  2                              :            46058
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.15
 p-value of test no 119                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.25
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.09
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.13
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.07
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.58
 p-value of test no 125                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.99
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.93
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9968
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.06
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.22
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.06
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.28
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.16
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.16
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.05
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.39
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.02
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.03
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.83
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.26
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.54
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.86
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.44
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.66
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.95
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.67
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.16
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.79
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.73
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.58
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.32
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.32
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.44
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.75
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.64
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.93
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.31
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.39
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.42
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.91
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9782.11
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.11
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
 p-value of test no 219                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5101.51
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.14
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.59
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.95
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.85
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.01
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.18
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000026251
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.35
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000111922
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:41.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97812510.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56196
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.37
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.40
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.93
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.44
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.57
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.85
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.67
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.31
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.37
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.63
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.90
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.01
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.40
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.36
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.83
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46218
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870218
   j =  1                              :        399907567
   j =  2                              :            46212
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907980
   j =  2                              :            46007
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 74                 :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.08
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.54
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.38
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.51
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.98
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.82
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.78
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.93
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.47
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.57
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.37
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.10
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.15
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.52
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.84
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.40
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.34
 p-value of test no 155                :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.41
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.10
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.12
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.97
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.75
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.20
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.53
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.31
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.91
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.25
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.53
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.58
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.03
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.29
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.36
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.09
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.87
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.89
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.86
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-4
 p-value of test no 193                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 195                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.05
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.10
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.26
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.00
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.18
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9746.17
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.055
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.22
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.06
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.88
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.12
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.29
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.13
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.30
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999937277
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.79
 p-value of test no 233                :  2.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000068755
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -2.46e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    2.44
 p-value of test no 249                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:47.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98828318.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56197
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.79
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.43
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.74
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.00
 p-value of test no 48                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.09
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.04
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.63
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.00
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.28
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 62                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.94
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.15
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.03
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908208
   j =  2                              :            45893
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45163
 p-value of test no 71                 :    0.9996    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869163
   j =  1                              :        399909676
   j =  2                              :            45159
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.36
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.65
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.21
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.59
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.33
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.64
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.98
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.28
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.81
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.24
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.22
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17251.87
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.29
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.61
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.17
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.68
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.36
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.18
 p-value of test no 152                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.45
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.26
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.02
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.57
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.40
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.21
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.68
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.77
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.36
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.31
 p-value of test no 164                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.47
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.29
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.05
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.65
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.83
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.30
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.06
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.97
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.48
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.10
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.80
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.80
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 185                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.55
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.15
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.80
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.59
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.00
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5062.43
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.50
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.70
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.48
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.41
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.67
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.00
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999985010
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.57
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000021553
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:02.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  45  CollisionPermut, r = 10         0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99844126.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56198
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1484
 p-value of test no 11                 :  7.2e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334604
   j =  1                              :        599997032
   j =  2                              :             1484
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.24
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.15
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.09
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.73
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.55
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.45
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.26
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.44
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.86
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.96
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.07
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.32
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908489
   j =  2                              :            45751
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46275
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870275
   j =  1                              :        399907453
   j =  2                              :            46269
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 79                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.39
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.27
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.84
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.19
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.08
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.44
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.21
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.31
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.42
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.41
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.07
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.59
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.97
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.69
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.07
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.42
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.57
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.84
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.52
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.93
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.87
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.17
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.42
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.22
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.12
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.14
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.54
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.79
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.70
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.29
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.67
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.85
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.27
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.62
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.76
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.25
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.45
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.16
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.15
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.27
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.33
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
 p-value of test no 201                :    0.9976
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.59
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.80
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.87
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.12
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.28
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.40
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.71
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.07
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.03
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11479.06
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.27
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999974552
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.84
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000038881
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:34.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           7.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100859934.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56199
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.33
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9961
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.19
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.40
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.58
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.46
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.91
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.63
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.51
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7248.35
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.29
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.40
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.09
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.00
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.01
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46198
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870198
   j =  1                              :        399907607
   j =  2                              :            46192
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908089
   j =  2                              :            45954
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -1.29e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.15
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.88
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.75
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.31
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.54
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.69
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.29
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.30
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.22
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.54
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.07
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.61
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.76
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.75
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.65
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.56
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.53
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.17
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.59
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.37
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.35
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.27
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.26
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.50
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.44
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.40
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.36
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.74
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.00
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.73
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.06
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.82
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.08
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.21
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.45
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.73
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.45
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.62
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.99
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.30
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.03
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.38
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.80
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.84
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.92
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.63
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.17
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.30
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.70
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.32
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.42
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999986021
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.00
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000051076
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 248                :    0.54
 
 Sample variance                       :    2.44
 p-value of test no 249                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:29.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101875742.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56200
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 9                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5536
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.69
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.89
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.51
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.13
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.23
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.61
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  281.07
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.67
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.59
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.53
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.59
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 62                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.00
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.27
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.89
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.25
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908195
   j =  2                              :            45898
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908232
   j =  2                              :            45878
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.99
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.48
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.56
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.77
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.19
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.70
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.32
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.82
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.36
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.14
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.88
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.27
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.44
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.47
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.40
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.28
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.79
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.29
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.51
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.71
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.22
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.85
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.04
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.78
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.68
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.29
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.53
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.64
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.88
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.59
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.68
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.92
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.00
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.46
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.72
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.25
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.85
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.87
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.88
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.97
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.54
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.84
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.86
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9730.51
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.80
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 221                :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.44
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.98
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.81
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.41
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.82
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.88
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.74
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000058537
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.61
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000012238
 
 Normal statistic for number of bits   :   0.097
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:46.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 81920000.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56201
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 11                 :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5206
 p-value of test no 13                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 44                 :    0.9966
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.88
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.07
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.97
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.53
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.65
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.85
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.87
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.14
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.02
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.75
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.1e-3
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 60                 :  7.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.59
 p-value of test no 61                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
 p-value of test no 62                 :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   97.25
 p-value of test no 65                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.34
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.55
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.96
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908539
   j =  2                              :            45729
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908101
   j =  2                              :            45942
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.20
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.96
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.76
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.81
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.98
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.81
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.63
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.67
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.19
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17240.54
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.05
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.27
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.65
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.51
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.62
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.98
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.51
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.34
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.46
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.91
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.75
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.13
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.58
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.97
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.66
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.35
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.65
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.58
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.65
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.96
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.76
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.54
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.05
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.16
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.16
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.87
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.43
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.95
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.16
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.17
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.62
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.04
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.44
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.22
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.06
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.82
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.07
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.96
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.18
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.57
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.46
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000052750
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.74
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999808412
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:04.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83558400.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56202
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7076
 p-value of test no 21                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9926
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.72
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.15
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.05
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.66
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.16
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.40
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.45
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.02
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.41
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.90
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46351
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907300
   j =  2                              :            46347
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908280
   j =  2                              :            45857
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 86                 :  7.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    5.77
 p-value of test no 88                 :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9992    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.75
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.64
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.94
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.53
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.51
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.11
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.13
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.35
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.25
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.54
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.88
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17216.54
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.30
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.49
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.83
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.38
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.05
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.34
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.76
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.67
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.17
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.24
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.61
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.83
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.68
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.05
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.82
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.33
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.28
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.08
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.73
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.80
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.66
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.80
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.93
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.00
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.38
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.68
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.72
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.20
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.67
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.47
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    2.28
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.50
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.87
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.65
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.84
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.69
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.48
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.84
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4282.87
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.01
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12075.88
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.55
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.29
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000092059
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.39
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999950753
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.16
 p-value of test no 239                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.81
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:36.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84377600.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56203
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 10                 :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.93
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.14
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.66
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.45
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.31
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.61
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.52
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.36
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6837.62
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.07
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.65
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.66
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.31
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.86
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908348
   j =  2                              :            45820
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.54
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.33
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.86
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.10
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.98
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.79
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.093
 p-value of test no 134                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.08
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.68
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.70
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.24
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.48
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.31
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.67
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.14
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.94
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.93
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.43
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.90
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.48
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.71
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.48
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.71
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.79
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.65
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.08
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.54
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.86
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.26
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.36
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.68
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.47
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.66
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.65
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.95
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.32
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.58
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.47
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.43
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.58
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.71
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.38
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.85
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.67
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.18
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.77
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999871016
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.42
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999893207
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    2.13
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:25.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           9.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85065728.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56204
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 11                 :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.95
 p-value of test no 35                 :  9.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.02
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.09
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.15
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.48
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.04
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.62
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.19
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.61
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.92
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.10
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.92
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.29
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.53
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.53
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.01
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907959
   j =  2                              :            46019
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908832
   j =  2                              :            45575
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.32
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.84
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.85
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.50
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.01
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.82
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.31
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.96
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.00
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.55
 p-value of test no 147                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.12
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.70
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.65
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.92
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.07
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.96
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.71
 p-value of test no 156                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  575.53
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.07
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.64
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.24
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.87
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.62
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.17
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.43
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.28
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.09
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5305.75
 p-value of test no 168                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.91
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.62
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.19
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.72
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.18
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.73
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.52
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.31
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.75
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.64
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.13
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.91
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 225                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5110.23
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4285.64
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.35
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.74
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.22
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.11
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999810365
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.00
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999939617
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 235                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.11
 p-value of test no 239                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 246                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.22
 p-value of test no 249                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:27.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86081536.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56205
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.61
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.70
 p-value of test no 47                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.13
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.25
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.18
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.42
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.29
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.82
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.37
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6799.56
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.92
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.05
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.81
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.30
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.07
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908521
   j =  2                              :            45735
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46223
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870223
   j =  1                              :        399907558
   j =  2                              :            46215
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-5
 p-value of test no 110                :    0.9931
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 116                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.67
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.67
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.17
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.28
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.07
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.18
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.39
 p-value of test no 125                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.89
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.36
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.94
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 142                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 143                :  8.9e-4    *****
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 144                :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17960.51
 p-value of test no 145                :  2.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.01
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.27
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.90
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.33
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.43
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.54
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.25
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.40
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.56
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.17
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.12
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.26
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.71
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.30
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.42
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.25
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.05
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.57
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.60
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.79
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.64
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.44
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.18
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.19
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.74
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.87
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.97
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.68
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.62
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.16
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.23
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.03
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9753.84
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9784.32
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.25
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.96
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.21
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.26
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.70
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.70
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.59
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.78
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999965687
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.58
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000143488
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:29.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87228416.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56206
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.52
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.91
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.79
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.46
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.20
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.01
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.33
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.04
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.19
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.02
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.99
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.72
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.86
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.60
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.85
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4817.75
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907692
   j =  2                              :            46151
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907775
   j =  2                              :            46111
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
 p-value of test no 77                 :    0.9966
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.02
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.05
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.85
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.07
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.97
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.81
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.20
 p-value of test no 134                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.40
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17547.20
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.17
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.36
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.67
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.38
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.25
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.58
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.81
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.34
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.28
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.25
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  193.62
 p-value of test no 159                :  8.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.90
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.89
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.89
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.57
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.98
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.92
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.49
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.53
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.67
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.48
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.25
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.72
 p-value of test no 171                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.69
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.27
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.12
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.04
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.29
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.06
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.02
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.81
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.94
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.01
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.86
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.85
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.19
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.53
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.90
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.72
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.14
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.06
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999917159
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.07
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999958079
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 250                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 251                :    0.9906
 
 Anderson-Darling statistic = A2       :    5.26
 p-value of test no 252                :  2.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.14
 p-value of test no 253                :    0.9991    *****
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:25.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     8.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  106  AutoCor, d=3, r=27              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88113152.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56207
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 22                 :    0.9984
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 23                 :    0.9974
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    3.56
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9927
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.13
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.73
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.71
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.82
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.64
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.98
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.43
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.17
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.21
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.45
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.08
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.01
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.13
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.65
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.77
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907977
   j =  2                              :            46010
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908195
   j =  2                              :            45901
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-5
 p-value of test no 109                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.56
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.80
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.18
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.59
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.10
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.85
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.72
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.93
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.37
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.12
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.30
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.76
 p-value of test no 146                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.42
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.79
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.18
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.01
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.33
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.77
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.85
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.26
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.05
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.33
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.36
 p-value of test no 157                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.10
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.60
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.21
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.56
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.24
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.70
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.56
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.05
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.91
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.10
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.74
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.90
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.93
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.92
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.50
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.39
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.98
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.34
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.63
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.04
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.11
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.18
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.26
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.07
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.50
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.87
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.43
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.49
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.04
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.20
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000031465
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.22
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999934598
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:41.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89128960.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56208
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.16
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.97
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.94
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.84
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  281.74
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.75
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.19
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.76
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.40
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.47
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.14
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.06
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.55
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908176
   j =  2                              :            45906
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908146
   j =  2                              :            45921
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.44
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.07
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.14
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.27
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.36
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.78
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.72
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.59
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.58
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.02
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17234.52
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.77
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.95
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.69
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.14
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.11
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.72
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.27
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.67
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.92
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.39
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.12
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.91
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.36
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.69
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.53
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.44
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.44
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.09
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.56
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.31
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.87
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.54
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.51
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.07
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.01
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.01
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.40
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.46
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.99
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.53
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.42
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.65
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.30
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5132.77
 p-value of test no 226                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.94
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3952.93
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.12
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.39
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.99
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000153541
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.75
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000009223
 
 Normal statistic for number of bits   :   0.073
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:24.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90144768.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56209
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 27                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9905
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.77
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.60
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.22
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.79
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.53
 p-value of test no 50                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.00
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.17
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.64
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.86
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.55
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.77
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.31
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.62
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  161.59
 p-value of test no 67                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.06
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908248
   j =  2                              :            45870
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45667
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869667
   j =  1                              :        399908673
   j =  2                              :            45653
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 86                 :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    6.26
 p-value of test no 88                 :  7.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9996    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.64
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.32
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.71
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.24
 p-value of test no 122                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.23
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.39
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.11
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.66
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.95
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.66
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17773.28
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.13
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.95
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.63
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.22
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.10
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.10
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.14
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.68
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.21
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.77
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.83
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.39
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.85
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.93
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.83
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.89
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.37
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.01
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.39
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.81
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.77
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.71
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.80
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.02
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.90
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.15
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.38
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10287.41
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.86
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5025.85
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.65
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.32
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.99
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11617.25
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.22
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.58
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999977483
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.35
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999936365
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:35.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91127808.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56210
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4184
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.59
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.67
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.11
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.47
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.28
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.19
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.08
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.74
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.59
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.78
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7377.70
 p-value of test no 57                 :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.09
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.26
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.49
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.61
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908026
   j =  2                              :            45984
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908459
   j =  2                              :            45763
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-5
 p-value of test no 109                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.92e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.68
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.35
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.74
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.95
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.57
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.93
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.76
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.23
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.11
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.07
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.35
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17475.13
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.27
 p-value of test no 146                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.60
 p-value of test no 147                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.92
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.72
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.09
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.75
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.90
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.17
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.46
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.18
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.35
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.15
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.42
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.08
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.62
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.99
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.56
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.31
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.42
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.91
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.55
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.17
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.97
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.54
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.92
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.93
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.10
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.29
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.17
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    2.36
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.51
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.49
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.96
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.97
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.26
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.44
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.22
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.31
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.93
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.70
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.55
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.02
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.94
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000080323
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.94
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000049366
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.090
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:43.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92143616.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56211
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.97
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9953
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.93
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.50
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.56
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.00
 p-value of test no 52                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.57
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.91
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.17
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.41
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.71
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.42
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.04
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.68
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.79
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45579
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869579
   j =  1                              :        399908847
   j =  2                              :            45569
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907859
   j =  2                              :            46063
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.91
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.89
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.95
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.15
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.09
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.27
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.72
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.15
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.71
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17591.85
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.04
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.58
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.86
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.92
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.70
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.33
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.69
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.50
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.07
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.54
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.97
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.28
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.86
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.25
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.11
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.23
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.71
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.23
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.01
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.77
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.98
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.26
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.30
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.99
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.38
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.78
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.65
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.17
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.90
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.44
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.95
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.24
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.70
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.47
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.60
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.98
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.99
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.25
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.68
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.22
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.04
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.67
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999948797
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.27
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000099424
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    2.15
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:29.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93159424.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56212
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.41
 p-value of test no 40                 :  2.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.50
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.08
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.19
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.19
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.23
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.69
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.47
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.89
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.22
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.47
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.54
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.64
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.41
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.88
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46187
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870187
   j =  1                              :        399907631
   j =  2                              :            46177
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 106                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.41
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.26
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.52
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.65
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.74
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.34
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.10
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.17
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.95
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.07
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17491.81
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.95
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.33
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.91
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.66
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.99
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.28
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.98
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.25
 p-value of test no 155                :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.83
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.85
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.35
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.24
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.39
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.15
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.83
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.44
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.14
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.48
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.51
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.61
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4840.54
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.82
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.11
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.88
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.61
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.84
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.05
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.71
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.88
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.76
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.79
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.78
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.37
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.98
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9662.28
 p-value of test no 215                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.75
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.83
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.17
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.00
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.67
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12082.31
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.05
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999976901
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.38
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000128680
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.88
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:52.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94142464.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56213
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    5.44
 p-value of test no 27                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.34
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.52
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.29
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   19.66
 p-value of test no 52                 : 1 -  4.7e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.38
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.17
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.50
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.54
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.07
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.08
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.93
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.35
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5226.85
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908239
   j =  2                              :            45876
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908447
   j =  2                              :            45772
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.12
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.78
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.97
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.65
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.67
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.17
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17355.35
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.74
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.02
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.13
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.94
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.51
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.94
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.44
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.39
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.97
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.63
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.66
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.51
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.64
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.43
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.83
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.76
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.05
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.09
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.82
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.91
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.42
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.95
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.97
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.72
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.34
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.13
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.31
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.97
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.17
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.80
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.30
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.69
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.80
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.00
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.52
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.17
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.80
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.66
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.29
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.46
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.54
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.65
 p-value of test no 231                :    0.9972
 
 
 -----------------------------------------------
 Total number of bits:  7999949607
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.66
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000015409
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 240                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.93
 p-value of test no 243                :  1.7e-3
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 246                :    0.9948
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    3.42
 p-value of test no 254                :  3.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:56.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20        1 -  4.7e-6
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95191040.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56214
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7544
 p-value of test no 15                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9931
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.37
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.64
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.56
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.40
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.19
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.89
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.86
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.91
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.19
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.23
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.04
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.51
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.10
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908405
   j =  2                              :            45796
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908643
   j =  2                              :            45668
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.23
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.15
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.51
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.61
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.11
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.96
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.52
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.02
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.48
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.85
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.70
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.72
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.97
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.59
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.16
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.20
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.04
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.00
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.40
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.42
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.51
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.75
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.49
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.00
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.27
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.23
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.68
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.47
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.46
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.98
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.51
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.22
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.57
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.52
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.30
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.62
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.70
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.41
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.34
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.04
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.47
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.65
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.44
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.75
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.74
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4727.57
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.06
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3877.10
 p-value of test no 227                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.89
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.29
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.52
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.97
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999999347
 
 Normal statistic for number of bits   : -5.16e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.69
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999923741
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 240                : 1 -  8.4e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 242                :  3.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.30
 p-value of test no 243                :  4.8e-4    *****
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:44.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  104  AutoCor, d=3, r=0               4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96206848.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56215
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.60
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.94
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.46
 p-value of test no 48                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.52
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.95
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.90
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.13
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.77
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6945.28
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.09
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.81
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.49
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.80
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.20
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908173
   j =  2                              :            45906
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908518
   j =  2                              :            45735
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 101                :    0.9928
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.08
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.67
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.07
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.28
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.19
 p-value of test no 123                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.24
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.17
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.21
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.06
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.22
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.69
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.64
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.09
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.46
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.83
 p-value of test no 149                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.38
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.45
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.58
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.64
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.87
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.10
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.89
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.46
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.99
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.24
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.16
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.10
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.35
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.82
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.31
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.89
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.97
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.53
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.26
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.27
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.38
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.88
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.38
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.12
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.38
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.38
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.92
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.64
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.22
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.84
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.66
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.53
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.64
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.62
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.62
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.89
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.90
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000074956
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.04
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999942167
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:22.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97222656.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56216
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.80
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.77
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.11
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.82
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.28
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.20
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.91
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.16
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.38
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.62
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.22
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.54
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.65
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.67
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.42
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908039
   j =  2                              :            45973
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908727
   j =  2                              :            45629
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.82
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.15
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.21
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.62
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.56
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.34
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.68
 p-value of test no 125                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.67
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.49
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.14
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 143                :    0.9941
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16997.52
 p-value of test no 145                :    0.9902
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.68
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.31
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.13
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.94
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.14
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.43
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.76
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.98
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.36
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.51
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.28
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.19
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.55
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.25
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.78
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.53
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.01
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.39
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.98
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.93
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.42
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.08
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.67
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.23
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.72
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.23
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.55
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.80
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.21
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.90
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.05
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.61
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.84
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.58
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5063.71
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.41
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.48
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.93
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.65
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.51
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999961148
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.95
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000021070
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 240                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:01.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98238464.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56217
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 7                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5222
 p-value of test no 13                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.21
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.64
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.84
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.89
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.14
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.24
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.51
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.43
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.74
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.23
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.17
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.69
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.66
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908593
   j =  2                              :            45699
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908713
   j =  2                              :            45633
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.10
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.85
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.22
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.76
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.81
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.75
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.55
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.94
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.07
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.95
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.53
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.92
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.91
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.08
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.61
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.14
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.82
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.64
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.94
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.92
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.47
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.46
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.86
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.18
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.88
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.75
 p-value of test no 167                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.76
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.14
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.06
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.53
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.44
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.20
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.93
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.23
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.17
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.93
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.30
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.35
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9704.01
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.17
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.44
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.26
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.56
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.04
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.82
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.63
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.50
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999937535
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.02
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000113917
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:35.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99254272.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56218
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4198
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7527
 p-value of test no 18                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     833
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.95
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.13
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.47
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.16
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.11
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.12
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.94
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.27
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6709.96
 p-value of test no 57                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.33
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.28
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.47
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.79
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.20
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46328
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870328
   j =  1                              :        399907349
   j =  2                              :            46318
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46150
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907703
   j =  2                              :            46144
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.84
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.75
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.99
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.59
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.57
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.44
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.06
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 143                :    0.9927
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17029.43
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.84
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.40
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.80
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.70
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.82
 p-value of test no 152                :  9.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.00
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.10
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.52
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.31
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.26
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.04
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.16
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.42
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.14
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.06
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.35
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.73
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.27
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.51
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.52
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.25
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.29
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.97
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4729.60
 p-value of test no 173                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.43
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.29
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.11
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.27
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.10
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.20
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.19
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.97
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.08
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.32
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.66
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.72
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.21
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.68
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000049009
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.60
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000119959
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:34.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100237312.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56219
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.74
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.11
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.24
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.72
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.63
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.16
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.21
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.40
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.48
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.03
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   77.32
 p-value of test no 67                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.72
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908348
   j =  2                              :            45823
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908637
   j =  2                              :            45677
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.35
 p-value of test no 115                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.22
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.63
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.84
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.78
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.82
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.21
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.30
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.48
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.89
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.84
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.97
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.91
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.37
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.33
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.15
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.90
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.55
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.17
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.45
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.36
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.56
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.32
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.01
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.14
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.19
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.05
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.75
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.27
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.59
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.36
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.24
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.19
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.31
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.71
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.41
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.18
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.04
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.81
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.33
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.91
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.56
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 182                :    0.9995    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.75
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.29
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.61
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.51
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.70
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.79
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.45
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.21
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.07
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.29
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.36
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000015832
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.67
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999979715
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:23.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  55  SampleCorr, k = 1               0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101253120.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56220
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 28                 :    0.9968
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.63
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.65
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.81
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.91
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.37
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.55
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.24
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.92
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.90
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.12
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.21
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.86
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.27
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.68
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908830
   j =  2                              :            45579
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45430
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869430
   j =  1                              :        399909144
   j =  2                              :            45422
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-3
 p-value of test no 86                 :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-3
 p-value of test no 90                 :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 91                 :  3.3e-3
 
 Anderson-Darling statistic = A2       :    5.57
 p-value of test no 92                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 104                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.31
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.18
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.42
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.64
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.92
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.94
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.54
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.21
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.06
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.92
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.00
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.63
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.83
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.79
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.31
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.47
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.86
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.01
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.71
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.96
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.47
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.25
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.49
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.36
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.94
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.72
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.94
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.05
 p-value of test no 167                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.38
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.16
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.34
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.27
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.86
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.60
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.55
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.79
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.49
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.06
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.89
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 209                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9751.92
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10247.24
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.62
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.39
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.44
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.33
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.62
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.80
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.16
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999994262
 
 Normal statistic for number of bits   :  -0.045
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.43
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999881693
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.013
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:43.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 81952769.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56221
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 8                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.67
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9941
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.30
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.96
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.52
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.41
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.37
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.05
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.40
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.77
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.33
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.63
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.88
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7153.31
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.30
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.01
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.04
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.57
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.37
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46159
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907685
   j =  2                              :            46153
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907840
   j =  2                              :            46074
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.31
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.95
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.72
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.61
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.28
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.89
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.82
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.09
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.12
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.59
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.61
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.67
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.98
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.69
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.44
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.00
 p-value of test no 152                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.96
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.31
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.25
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.83
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.53
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.87
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.67
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.47
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.94
 p-value of test no 165                :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.99
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.71
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.18
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.65
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.75
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.57
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.79
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.03
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.20
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.23
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.40
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.54
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 180                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.77
 p-value of test no 183                :  2.8e-3
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.13
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.38
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.79
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.73
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.02
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.80
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.22
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.72
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.77
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.83
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.46
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.22
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000075937
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.64
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999895874
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.70e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:25.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83525633.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56222
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    4.65
 p-value of test no 27                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.89
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.24
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.46
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.50
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.82
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.26
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.99
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.34
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.41
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.82
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.73
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.04
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.50
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908237
   j =  2                              :            45874
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908676
   j =  2                              :            45656
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.92
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.09
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.21
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.74
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.06
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.02
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.15
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17712.32
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.76
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.72
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.16
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.76
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.77
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.41
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.93
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.49
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.77
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.78
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.65
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.85
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.74
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.76
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.92
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.33
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.64
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.40
 p-value of test no 164                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.61
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.80
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.99
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.46
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.04
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.85
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.05
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.93
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.91
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.96
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.97
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.45
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.81
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    2.15
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.36
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.47
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.38
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.22
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 220                :    0.9920
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4674.40
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.70
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4373.99
 p-value of test no 227                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.19
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.62
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12127.42
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.38
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000199345
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.19
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000067141
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:38.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84180993.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56223
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 6                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.75
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.10
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.92
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.82
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.14
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.66
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.20
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.20
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.51
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.73
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6890.54
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.96
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.72
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.76
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.32
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908167
   j =  2                              :            45912
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908722
   j =  2                              :            45633
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   34.63
 p-value of test no 119                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.43
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.25
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.08
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.70
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.97
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.40
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.95
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.51
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.00
 p-value of test no 135                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.52
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17601.73
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.13
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.75
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.68
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.63
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.18
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.05
 p-value of test no 152                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.70
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.48
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.89
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.95
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.29
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.61
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.02
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.40
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.08
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.95
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.77
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.22
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.02
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.51
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.38
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.17
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.20
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.45
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.73
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.22
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.80
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.99
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.66
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.26
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.77
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.14
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.27
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.54
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.39
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.35
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5103.16
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.58
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.90
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.03
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11536.74
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.24
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000024103
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.07
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000054709
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:43.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85458945.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56224
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.53
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    3.20
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     256
 p-value of test no 37                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.13
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.01
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.30
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.15
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.69
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.16
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.15
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.76
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.80
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.12
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.66
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.14
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.11
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4812.41
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907913
   j =  2                              :            46039
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908015
   j =  2                              :            45988
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 80                 :  3.7e-3
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.60
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.91
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.95
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.95
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.61
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.33
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.71
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.80
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.74
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17673.14
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.97
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.15
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.70
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.70
 p-value of test no 150                :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.66
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.24
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.90
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.89
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.81
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.64
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.27
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.26
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.27
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.76
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.39
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.32
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.62
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.90
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.30
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.46
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.03
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.06
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.38
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.34
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.76
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.38
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.57
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.60
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.62
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.98
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.12
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.72
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.86
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.15
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.78
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.59
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.03
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.82
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.30
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000099973
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.23
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999967709
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.062
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.097
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:50.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86409217.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56225
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1485
 p-value of test no 9                  :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.13
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.30
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.34
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.29
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.34
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.07
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.74
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.87
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.70
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.67
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.34
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.66
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.50
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.26
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.43
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45492
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869492
   j =  1                              :        399909025
   j =  2                              :            45474
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45656
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869656
   j =  1                              :        399908691
   j =  2                              :            45650
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.67
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.22
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.66
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.11
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.57
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.31
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.72
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.42
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.59
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.37
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.92
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.35
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.49
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.59
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.60
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.22
 p-value of test no 152                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.22
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.86
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.00
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.53
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.13
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.26
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.42
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.25
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.32
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.63
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.19
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.90
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.29
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.65
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.20
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.96
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.77
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.69
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.64
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.60
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.64
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.92
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.80
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.98
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.48
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.81
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.31
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.08
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.12
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.96
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.29
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.61
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.64
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11368.10
 p-value of test no 230                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.02
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000064153
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.57
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999993452
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:18.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           6.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87523329.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56226
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 12                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4511
 p-value of test no 14                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.58
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.56
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.02
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.33
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.40
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.26
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.59
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.65
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.99
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.18
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.04
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   85.96
 p-value of test no 67                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.96
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908100
   j =  2                              :            45944
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908065
   j =  2                              :            45963
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 84                 :    0.9902
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.88
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.26
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.26
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.27
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.98
 p-value of test no 123                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.08
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.71
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.85
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.01
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.78
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17110.21
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.57
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.53
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.75
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.97
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.18
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.48
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.44
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.06
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.20
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.77
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.14
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.30
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.96
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.14
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.31
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.98
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.33
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.99
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4761.13
 p-value of test no 168                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.97
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.79
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.66
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.85
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.52
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.30
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.03
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.58
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.21
 p-value of test no 189                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.48
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.95
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.74
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.47
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.78
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.91
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.24
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.34
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4367.04
 p-value of test no 227                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.03
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.13
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.29
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.85
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000042304
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.20
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999997529
 
 Normal statistic for number of bits   :  -0.020
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:19.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88702977.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56227
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.01
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.20
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.83
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.68
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.38
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.89
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.12
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.13
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.94
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.41
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.71
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.92
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.92
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.90
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.57
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908480
   j =  2                              :            45754
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908130
   j =  2                              :            45926
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.2e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.86
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.50
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.51
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.36
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.36
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.45
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.51
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.80
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.05
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.04
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.62
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.07
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.82
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.00
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.18
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.18
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.18
 p-value of test no 154                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.62
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.11
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.12
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.82
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.21
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.13
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.23
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.48
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.55
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.53
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.70
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.15
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.06
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.48
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.16
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.19
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.08
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5242.46
 p-value of test no 173                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.10
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.16
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.82
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.03
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.07
 p-value of test no 198                :  7.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.80
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.99
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.45
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.84
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.80
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.83
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.59
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.43
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.67
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.66
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.64
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000119092
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.68
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000126361
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:30.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89718785.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56228
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    3.88
 p-value of test no 38                 :  1.0e-2
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.21
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  299.50
 p-value of test no 54                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.03
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.65
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.47
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.75
 p-value of test no 59                 :  1.0e-3
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.43
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.81
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.89
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.16
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.35
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46194
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870194
   j =  1                              :        399907616
   j =  2                              :            46186
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46173
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907659
   j =  2                              :            46163
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 87                 :    0.9936
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.03
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.85
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.22
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.71
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.35
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.51
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  8.8e-3
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.14
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.28
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.09
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.16
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17068.70
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.25
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.84
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.72
 p-value of test no 149                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.36
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.57
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.84
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.93
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.32
 p-value of test no 156                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.57
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.51
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.30
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.43
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.67
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.90
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.67
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.22
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.23
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.91
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.71
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.10
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.22
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.25
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.83
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.92
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.21
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.06
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.40
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.88
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.48
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.90
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 208                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10370.87
 p-value of test no 211                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.33
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.44
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.05
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.07
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.22
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.29
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.15
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.34
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000038656
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.38
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999925637
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:16.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90734593.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56229
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 35                 :    0.9984
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.54
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.49
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.78
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.59
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.45
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.53
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.99
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1329.63
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.89
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.56
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.70
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.12
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.59
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907882
   j =  2                              :            46059
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907893
   j =  2                              :            46052
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.63
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.79
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.65
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.05
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.42
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.68
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.48
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.24
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.51
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.78
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.31
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.85
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.80
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.63
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.94
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.68
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.86
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.72
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.84
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.41
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.88
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.29
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.62
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.49
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.54
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.46
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.31
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.67
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.16
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.65
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.22
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.03
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.78
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.16
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.80
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.85
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.96
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.10
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.26
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.39e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.16
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.89
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.48
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.13
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.42
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.12
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.46
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.11
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.60
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.43
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.30
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.55
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.79
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999965426
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.26
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000024706
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:56.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91684865.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56230
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.09
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9935
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.07
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.34
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.01
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.25
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.96
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.16
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.81
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.92
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.48
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.35
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.17
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.03
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.13
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907896
   j =  2                              :            46046
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908591
   j =  2                              :            45700
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 115                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.77
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.88
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.76
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.95
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.85
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.31
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.64
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.95
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.05
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.96
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.00
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.81
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.47
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.82
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.40
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.72
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.55
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.90
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.52
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.13
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.46
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.07
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.91
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.88
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.40
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.14
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.41
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.81
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  126.47
 p-value of test no 165                :  1.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.97
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.82
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.50
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.87
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.52
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.02
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.31
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.80
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.96
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.85
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.45
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.45
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.87
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.68
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9754.83
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.00
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.62
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5072.60
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.16
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.88
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.52
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.30
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.78
 p-value of test no 231                :  3.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999934274
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.60
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000282586
 
 Normal statistic for number of bits   :    2.23
 p-value of test no 234                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:36.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    1.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92700673.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56231
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 11                 :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.65
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.67
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.75
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.00
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.12
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.13
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.46
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.67
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.03
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6859.03
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.19
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.31
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.90
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.87
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907928
   j =  2                              :            46033
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908523
   j =  2                              :            45734
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.77
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.99
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.32
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.91
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.94
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.87
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.17
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.80
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.74
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.21
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.59
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.21
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.96
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.05
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.30
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.31
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.23
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.20
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.57
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.91
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.00
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.23
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.41
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.91
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.98
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.24
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.21
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.63
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.74
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.05
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.62
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.13
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.10
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.32
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.80
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.99
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.17
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.08
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.14
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.25
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.88
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.72
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.91
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5046.28
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.94
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.72
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.97
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12067.56
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.13
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999947546
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.14
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000156451
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:07.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93585409.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56232
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.15
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.00
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.84
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.14
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.91
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.45
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.89
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.26
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.39
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.47
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.54
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.92
 p-value of test no 67                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5153.82
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46154
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870154
   j =  1                              :        399907694
   j =  2                              :            46150
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.93
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.88
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.84
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.42
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.65
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.26
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.46
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.01
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.89
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17304.81
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.91
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.58
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.30
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.57
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.22
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.51
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.98
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.33
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.64
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.72
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.23
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.83
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.50
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.29
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.77
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.67
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.98
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.51
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.41
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.04
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.87
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.32
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.30
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.95
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5239.21
 p-value of test no 173                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.16
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.74
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.08
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.65
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.68
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.80
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.04
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.34
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.67
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5114.91
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.22
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.98
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.30
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.41
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.02
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999934616
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.50
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999854732
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    2.07
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:31.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94568449.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56233
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 10                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5228
 p-value of test no 13                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    3.74
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    8.73
 p-value of test no 26                 :  5.5e-5    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.66
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.13
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.96
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.33
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.68
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.40
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.60
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.75
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.83
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.03
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.55
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907979
   j =  2                              :            46003
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46145
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907713
   j =  2                              :            46139
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.75
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.00
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.85
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.98
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.33
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.76
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.20
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.23
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.14
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.45
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.68
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.17
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.63
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.70
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.02
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.42
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.35
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.69
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.91
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.60
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.24
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.05
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.30
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.24
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.77
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.38
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.28
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.98
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.82
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.55
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.65
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.68
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.25
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.91
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.87
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.55
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.85
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.60
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.34
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.13
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.34
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.58
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.45
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12088.85
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.95
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999966710
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.91
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999841049
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:09.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          5.5e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95584258.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56234
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 12                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.47
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.20
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.90
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.79
 p-value of test no 51                 :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.76
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.88
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.33
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.84
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.16
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.08
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.31
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.98
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.25
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.06
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908176
   j =  2                              :            45906
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908553
   j =  2                              :            45722
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.9912
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.25
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.94
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.96
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.86
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.15
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.37
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.87
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.30
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.66
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.67
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.86
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.31
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.80
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.89
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.35
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.30
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.35
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.14
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.96
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.51
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.82
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.60
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.77
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.94
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.86
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.26
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.68
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.90
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.47
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.68
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.65
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.08
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.36
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.78
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.44
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 201                :    0.9927
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.43
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.20
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.15
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.03
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.71
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.57
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.60
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.58
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.24
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.50
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.83
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999998060
 
 Normal statistic for number of bits   :  -0.015
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.30
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000078931
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:00.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96665626.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56235
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.9916
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.37
 p-value of test no 40                 :  7.5e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    4.74
 p-value of test no 44                 :  3.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.10
 p-value of test no 46                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.13
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.75
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.34
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.52
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.11
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.96
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.13
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7287.86
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.84
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.29
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.58
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.38
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4834.99
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908657
   j =  2                              :            45664
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908739
   j =  2                              :            45626
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-3
 p-value of test no 84                 :    0.9974
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.36
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.65
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.97
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.80
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.81
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.53
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.32
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.47
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.08
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.34
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.28
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.62
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.49
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.54
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.22
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.10
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.26
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.60
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.27
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.95
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.88
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.36
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.17
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.92
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.35
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.46
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.83
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.19
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.91
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.67
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.76
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.04
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.46
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.88
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.61
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.33
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.68
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.18
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.97
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.48
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.05
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.07
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.28
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.25
 p-value of test no 218                :  5.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.96
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.75
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.81
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.88
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.61
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12055.49
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.36
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999928574
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.13
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999875072
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    2.21
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:44.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NP, t = 16           7.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  94  HammingCorr, L = 1200           5.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97681434.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56236
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 11                 :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9923
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.56
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.78
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.71
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.71
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.32
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.83
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1322.47
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.55
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.31
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.98
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.46
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.72
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908000
   j =  2                              :            45994
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908661
   j =  2                              :            45662
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.20
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.95
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.19
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.79
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.20
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.69
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.69
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.79
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.59
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.48
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17192.32
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.42
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.02
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.20
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.91
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.82
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.39
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.25
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.87
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.95
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.16
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.20
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.53
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.46
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.95
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.39
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.39
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.19
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.22
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.33
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.80
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.74
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.61
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.17
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.33
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.54
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.46
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.75
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.09
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.47
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.32
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.14
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.32
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.29
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.04
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.05
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.05
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.02
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.77
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.91
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.83
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.34
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000071560
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.46
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999972767
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    2.01
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:02.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98762778.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56237
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 11                 :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.29
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.27
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.13
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.10
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  284.75
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.66
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.33
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6993.33
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.29
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.77
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.18
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.02
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908189
   j =  2                              :            45901
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45642
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908718
   j =  2                              :            45638
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-4
 p-value of test no 109                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-5
 p-value of test no 110                :    0.9958
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 111                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.41
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.99
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.84
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.64
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.67
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.84
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.93
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.54
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.03
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.84
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.74
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.61
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.28
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.06
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.46
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.14
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.99
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.24
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.63
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.18
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.37
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.33
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.05
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.71
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.85
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.14
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.57
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.61
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.58
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.97
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.78
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.03
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.17
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.30
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.70
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.73
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10243.30
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.08
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.28
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.46
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.66
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3961.94
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.83
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.50
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.08
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000086059
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.31
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000104380
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.18
 p-value of test no 244                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:29.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99909658.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56238
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.63
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.97
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.70
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.52
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.70
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.14
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.70
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.06
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.09
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.97
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.50
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.76
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.28
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908090
   j =  2                              :            45949
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908617
   j =  2                              :            45687
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 97                 :  3.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 99                 :  5.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.86
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.59
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.20
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.48
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.37
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.49
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.59
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.58
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.46
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.33
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.80
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.85
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.26
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.72
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.89
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.36
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.34
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.47
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.35
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.82
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.02
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.58
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.62
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.93
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.84
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.10
 p-value of test no 162                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.76
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.88
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.50
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.57
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.08
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.31
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.35
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.74
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.57
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.01
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.53
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.43
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.74
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.88
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.17
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.23
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.87
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.73
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.09
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.41
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.22
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.36
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5099.66
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.87
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.85
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.95
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.00
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.26
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000198013
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.82
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999942539
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    2.74
 p-value of test no 239                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    2.43
 p-value of test no 254                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:37.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100892698.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56239
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 8                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    4.65
 p-value of test no 27                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.88
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.34
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.02
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.82
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.17
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.79
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.27
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.92
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.69
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.36
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.56
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.43
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.78
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45480
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909041
   j =  2                              :            45478
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908130
   j =  2                              :            45932
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 97                 :  2.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    9.58
 p-value of test no 99                 :  2.3e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.99
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.21
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.65
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.30
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 126                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.29
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.52
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.92
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 142                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17944.13
 p-value of test no 145                :  3.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.20
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.72
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.39
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.10
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.72
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.80
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.18
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.94
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.57
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.87
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.29
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.99
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.65
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.82
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.84
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.81
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.21
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.62
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.31
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.21
 p-value of test no 166                :    0.9974
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.95
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.15
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.51
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.94
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.26
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.56
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.06
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.43
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.05
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.50
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.83
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.03
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.98
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.59
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.72
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.66
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.95
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.33
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11525.47
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.59
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.52
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999976640
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.59
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000032443
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.73
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-3
 p-value of test no 241                :    0.9989
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 243                :    0.9939
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:41.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               2.3e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101941274.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56240
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.81
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.34
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.82
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.62
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.48
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.56
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.55
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.46
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.56
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.94
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    5.38
 p-value of test no 64                 :  2.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.46
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.10
 p-value of test no 66                 :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.88
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.65
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46183
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907644
   j =  2                              :            46163
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907865
   j =  2                              :            46066
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-5
 p-value of test no 109                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.33
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.52
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.94
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.48
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.69
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.25
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.28
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.89
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.02
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.15
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.76
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.00
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.33
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.66
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.74
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.64
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.36
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.83
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.80
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.89
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.64
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.70
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.18
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.61
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.60
 p-value of test no 161                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.95
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.95
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.62
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.00
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.58
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.36
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.78
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.15
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.79
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.18
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.11
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.48
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.92
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.03
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.08
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.86
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.05
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.88
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.84
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.56
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.51
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4727.53
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.19
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.24
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.35
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.32
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.83
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999981872
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.33
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000036553
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:41.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 81985538.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56241
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 9                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.82
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.62
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.72
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.35
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.06
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.88
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.69
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.85
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.93
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.41
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.26
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.37
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908645
   j =  2                              :            45673
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908357
   j =  2                              :            45814
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-4
 p-value of test no 100                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.80
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.70
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.95
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.64
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.05
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.79
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.12
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.37
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.70
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17305.26
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.93
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.24
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.08
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.23
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.73
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.29
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.43
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.65
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.36
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.48
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.65
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.50
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.45
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.10
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.80
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.33
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.98
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.47
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.12
 p-value of test no 166                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.89
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.97
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.34
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.04
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.89
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.90
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.63
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.57
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.49
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.05
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.46
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.15
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.57
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.06
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.43
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.40
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5112.55
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.81
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.57
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.68
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.90
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.17
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.46
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000061633
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.42
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000029419
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.62
 p-value of test no 238                :  4.4e-3
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:29.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83820546.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56242
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 7                  :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5575
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.42
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.91
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.79
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.92
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.24
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.84
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.14
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.88
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.90
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.09
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.64
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.93
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.68
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.54
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908328
   j =  2                              :            45833
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907859
   j =  2                              :            46063
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.08
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.47
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.15
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.25
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.14
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.16
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.87
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.14
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.77
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.67
 p-value of test no 134                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.20
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17664.24
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.89
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.44
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.07
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.15
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.47
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.81
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.07
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.44
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.48
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.61
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.92
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.23
 p-value of test no 160                :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.33
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.14
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.02
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.88
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.29
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.15
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.92
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.00
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.27
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.41
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.75
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.75
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.53
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.43
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.76
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.48
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.39
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.73
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.62
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.75
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 206                :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.48
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.05
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.03
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.26
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.37
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.21
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.35
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.61
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.55
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.26
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999921911
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.14
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000098404
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:10.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84672514.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56243
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1484
 p-value of test no 11                 :  7.2e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334604
   j =  1                              :        599997032
   j =  2                              :             1484
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.82
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.96
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.12
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.40
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.34
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.47
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.07
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.90
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.90
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6796.35
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.80
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.20
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.45
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.75
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4858.34
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908351
   j =  2                              :            45823
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907662
   j =  2                              :            46166
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.76
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.28
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.98
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.36
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.02
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.22
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.39
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.22
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.34
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.67
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17579.76
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.98
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.18
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.42
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.55
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.97
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.07
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.32
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.88
 p-value of test no 155                :    0.9940
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.16
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.88
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.62
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.70
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.04
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.58
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.52
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.45
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.36
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.93
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.77
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.04
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.80
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.40
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.49
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.39
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.63
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.53
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.19
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.94
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.17
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.27
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.84
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.48
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.68
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.37
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.20
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.67
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.39
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.15
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.60
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.47
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.44
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.03
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000017956
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.36
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000040534
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:28.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           7.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85590043.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56244
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.71
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.62
 p-value of test no 40                 :  4.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    3.18
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.74
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.90
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.17
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.25
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.14
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.58
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.68
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.01
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.80
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.73
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.20
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.58
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.01
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907884
   j =  2                              :            46052
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908448
   j =  2                              :            45770
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.07
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.83
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.04
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.51
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.30
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.63
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.92
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.90
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.33
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17275.23
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.85
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.57
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.41
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.79
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.73
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.79
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.53
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.53
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.46
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.44
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.93
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.21
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.96
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.09
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.52
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.48
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.09
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.36
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.72
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.12
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.36
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.45
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.98
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.36
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.29
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.83
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.66
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.96
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.63
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
 p-value of test no 205                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.43
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.18
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.58
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.87
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.19
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.47
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4394.51
 p-value of test no 228                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.33
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.36
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.13
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999940535
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.02
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999952874
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    2.35
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:21.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86835227.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56245
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 12                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.21
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.44
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.53
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.33
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.42
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.26
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7291.40
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.95
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.50
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.51
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.29
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908250
   j =  2                              :            45869
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908888
   j =  2                              :            45556
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.78
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.31
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.15
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.61
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.80
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.00
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.58
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.07
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17788.07
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.10
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.88
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.82
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.21
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.49
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.52
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.84
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.14
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.50
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.26
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.27
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.25
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.23
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.29
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.98
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.55
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.69
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.44
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.10
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.31
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.13
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.41
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.05
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.99
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.26
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.84
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.71
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.43
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.24
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.55
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 193                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.24
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.59
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.34
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.81
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.40
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.96
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5053.23
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.36
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.64
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.02
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.27
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.38
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999974297
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.27
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999976271
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:06.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87785499.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56246
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    3.21
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.75
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.49
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.66
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.17
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.11
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.72
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.91
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.89
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.61
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.26
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.23
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.25
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.37
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.10
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.90
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5184.14
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45615
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908773
   j =  2                              :            45609
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907860
   j =  2                              :            46061
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.08
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.17
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.33
 p-value of test no 121                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.24
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.11
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.07
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.62
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.12
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.85
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.68
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.71
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.43
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.50
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.10
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.57
 p-value of test no 148                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.19
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.26
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.60
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.30
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.18
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.65
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.82
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.60
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.89
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.42
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.22
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.69
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.56
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.05
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.39
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.92
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.56
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.34
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.18
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.19
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.76
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.70
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.63
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.20
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.79
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.40
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.73
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.16
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.02
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.62
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.00
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.03
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.43
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.67
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.76
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.71
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.64
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12015.32
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.27
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.44
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000028135
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.40
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000034258
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 240                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.037
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:52.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88768539.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56247
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    2.94
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.56
 p-value of test no 47                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.73
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.17
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.11
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.92
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.63
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.07
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.59
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.16
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.32
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.75
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.26
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4847.08
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46202
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870202
   j =  1                              :        399907599
   j =  2                              :            46196
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908527
   j =  2                              :            45735
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.39
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.82
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.63
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.45
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   70.85
 p-value of test no 123                :  6.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.15
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.97
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.82
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.84
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17621.66
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.24
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.82
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.82
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.41
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.12
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.08
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.48
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.27
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.57
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.31
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.41
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.73
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.30
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.92
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.62
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.77
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.51
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.39
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.01
 p-value of test no 167                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.35
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.10
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.08
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.13
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.83
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.10
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.75
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.80
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.97
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.42
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.60
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.59
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.01
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.52
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.69e-5
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.05
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.16
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.28
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.31
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.68
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.86
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.73
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000009946
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.78
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999971567
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 235                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    5.27
 p-value of test no 237                :  2.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.29
 p-value of test no 238                :  5.0e-4    *****
 
 Sample variance                       :    2.26
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.20
 p-value of test no 254                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:50.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           6.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  103  AutoCor, d=1, r=0               5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89882651.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56248
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.52
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.80
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.13
 p-value of test no 49                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.07
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.06
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.66
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.23
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.18
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.84
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.28
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7234.13
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.89
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.93
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.21
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.03
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908831
   j =  2                              :            45574
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45389
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869389
   j =  1                              :        399909224
   j =  2                              :            45385
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 87                 :    0.9931
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 88                 :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9990
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.92
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.54
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.06
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.91
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.09
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.54
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.59
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.43
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17533.07
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.03
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.56
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.92
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.88
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.81
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.87
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.95
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.19
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.98
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.69
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.79
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.71
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.04
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.23
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.99
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.56
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.21
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.00
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.74
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.36
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.69
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.45
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.81
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.54
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.92
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 181                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.56
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.41
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.79
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.80
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.07
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.09
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.82
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.54
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.45
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.05
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.15
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999982079
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.91
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000067570
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:57.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90865691.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56249
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 45                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.11
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.31
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.38
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.82
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.55
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.71
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.00
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.88
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.56
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.33
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.52
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.33
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.08
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.32
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.92
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908390
   j =  2                              :            45802
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908585
   j =  2                              :            45703
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-5
 p-value of test no 112                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   36.54
 p-value of test no 119                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.31
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.10
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.87
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.19
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.09
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.38
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.99
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.03
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.05
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.75
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.07
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.33
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.01
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.11
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.31
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.40
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.10
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.76
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.82
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.62
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.29
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.06
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.27
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.81
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.55
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.34
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.74
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.31
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.20
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.17
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.24
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.97
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.90
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.41
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.14
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.01
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.18
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.28
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.75
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.35
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9713.87
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9760.03
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.30
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.88
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.29
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.59
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.21
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.82
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.13
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999914081
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.17
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999968603
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 252                :    0.9993    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:47.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            0.9991 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91815963.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56250
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.83
 p-value of test no 23                 :  3.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.49
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.57
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.21
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.39
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.93
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.91
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.70
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.28
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.72
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.67
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.94
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.95
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.05
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.86
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907959
   j =  2                              :            46019
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907733
   j =  2                              :            46132
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  8.7e-3
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 88                 :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  2.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
 p-value of test no 91                 :    0.9973
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 92                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 100                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.27
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.96
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.51
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.66
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.53
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.82
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.50
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.16
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17685.26
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.87
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.46
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.43
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.52
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.46
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.32
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.29
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.83
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.23
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.67
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.49
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.69
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.58
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.39
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.53
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.89
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.11
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.32
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.01
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.70
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.94
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.50
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.93
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.18
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.84
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  505.69
 p-value of test no 174                :  1.2e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.92
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.52
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.41
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.09
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.10
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.83
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.14
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9732.37
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.59
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.70
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.24
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.50
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.36
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.35
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.31
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.87
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999943895
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.77
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999995927
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:34.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   1.2e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92766235.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56251
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    4.07
 p-value of test no 36                 :  8.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.66
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.70
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.94
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.09
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.55
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.45
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.96
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.09
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.55
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.18
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.59
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.60
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.00
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.20
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45421
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869421
   j =  1                              :        399909162
   j =  2                              :            45413
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908042
   j =  2                              :            45976
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.20
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.43
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.30
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.55
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.90
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.85
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.44
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.28
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.32
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.41
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.15
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.62
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.61
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.83
 p-value of test no 149                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.87
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.19
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.16
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.27
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.28
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.94
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.52
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.22
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.79
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.27
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.44
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.15
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.17
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.25
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.09
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.67
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.61
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.32
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.44
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.07
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.80
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.62
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.13
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.05
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.91
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.69
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.97
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.28
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.74
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.11
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.08
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.07
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.68
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.14
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.82
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999987500
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.33
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999973748
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.50e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:01.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93683739.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56252
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4172
 p-value of test no 14                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.02
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.35
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.43
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.29
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.95
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.40
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.63
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.20
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.93
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.95
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.27
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.66
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.76
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.36
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.67
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908853
   j =  2                              :            45563
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46301
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870301
   j =  1                              :        399907400
   j =  2                              :            46297
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.88
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.74
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.21
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.53
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.54
 p-value of test no 123                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.20
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.07
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.49
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.34
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.53
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.40
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.20
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.25
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.42
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.52
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.31
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.95
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.50
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.49
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.68
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.28
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.55
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.58
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.56
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.56
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.02
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.79
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.48
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.02
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.06
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.14
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.91
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.67
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.72
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.35
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.48
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.80
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.45
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.24
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.89
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.87
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.75
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.31
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.21
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.80
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3918.21
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.50
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.21
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.61
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   93.31
 p-value of test no 231                :  7.2e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000091117
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.38
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000016573
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:38.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  101  Run of bits, r = 0              7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94634011.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56253
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.76
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.67
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.64
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.52
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.55
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.70
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.07
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.90
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.19
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.15
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.07
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.15
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.95
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.85
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907918
   j =  2                              :            46038
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908304
   j =  2                              :            45839
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-4
 p-value of test no 93                 :    0.9990    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  6.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.66
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.86
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.57
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.07
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.25
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.01
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.58
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.37
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.01
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.90
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.10
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.18
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.33
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.98
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.70
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.46
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.85
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.32
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.35
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.63
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.32
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.35
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.94
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.16
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.84
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.48
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.04
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.94
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.27
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.05
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.96
 p-value of test no 170                :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.55
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.31
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.75
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.61
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.10
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.46
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.94
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.77
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.31
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.65
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.43
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.22
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.14
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.68
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.54
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000033478
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.63
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000096796
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 251                :    0.9959
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 252                :  6.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.02
 p-value of test no 253                :    0.9987
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:10.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95748123.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56254
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5230
 p-value of test no 13                 :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.78
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9930
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.23
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.37
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.22
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.25
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.54
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.62
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.44
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.32
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.14
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.89
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.71
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.01
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.56
 p-value of test no 66                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.61
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.15
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908613
   j =  2                              :            45689
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908086
   j =  2                              :            45954
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.68
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.03
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.84
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   68.78
 p-value of test no 122                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.96
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.64
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.80
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.55
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.91
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.86
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.67
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
 p-value of test no 142                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17810.66
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.80
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.56
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.88
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.25
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.19
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.15
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.73
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.07
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.25
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.51
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.08
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.47
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.05
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.94
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.95
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.60
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.22
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.55
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.29
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.08
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.41
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.92
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.86
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.14
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.99
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.23
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.65
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.83
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.33
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.94
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.21
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.10
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4723.55
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.90
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.88
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.97
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.38
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.35
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999941594
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.65
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000081298
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:30.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96698395.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56255
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 6                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.15
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.47
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.90
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.77
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.61
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  184.64
 p-value of test no 54                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  369.65
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.32
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.70
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.12
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.21
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.69
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.51
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.42
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45413
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869413
   j =  1                              :        399909175
   j =  2                              :            45411
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908296
   j =  2                              :            45846
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.0e-3
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-4
 p-value of test no 109                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 111                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.63
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.77
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.93
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.39
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.82
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.03
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.17
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.07
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.99
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.24
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.50
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.57
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.29
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.33
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.46
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.19
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.67
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.14
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.60
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.89
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.72
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.54
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.74
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.32
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.06
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.37
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.80
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.93
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.80
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.61
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.35
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.29
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.81
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.77
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.05
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.82
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.73
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.01
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.14
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.88
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.13
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10226.75
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.10
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.67
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.02
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.67
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.17
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.14
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.84
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000069331
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.56
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000044767
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:15.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97517595.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56256
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.92
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.74
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.57
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.77
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.17
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.18
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.49
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.11
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.26
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.77
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.17
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908178
   j =  2                              :            45908
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908704
   j =  2                              :            45645
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 99                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.68
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.34
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.86
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.18
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.66
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.15
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9970
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.41
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.69
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.29
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.09
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.33
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.73
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.03
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.32
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.38
 p-value of test no 149                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.67
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.71
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.44
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.00
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.62
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.49
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.17
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.34
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.28
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.90
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.95
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.29
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.21
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.82
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.38
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.11
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.69
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.75
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.96
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.22
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.24
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.34
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.79
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.88
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.75
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.58
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.79
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.28
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.51
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.72
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.65
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.25
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11566.39
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.08
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.81
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000050887
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.84
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999975536
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.62
 
 Sample variance                       :    2.83
 p-value of test no 249                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:30.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98533403.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56257
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.68
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.86
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.06
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.72
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.40
 p-value of test no 53                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.87
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.92
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.64
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.67
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.14
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.68
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.56
 p-value of test no 67                 :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.65
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908486
   j =  2                              :            45751
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46093
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907816
   j =  2                              :            46089
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
 p-value of test no 83                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.9e-3
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 85                 :  6.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.70
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.83
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.28
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.98
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.24
 p-value of test no 124                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.43
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.69
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.58
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.38
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.84
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.94
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.32
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.92
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.99
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.92
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  583.42
 p-value of test no 158                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.09
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.52
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.64
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.23
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.20
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.67
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.61
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.73
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.67
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.97
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.68
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.50
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.07
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.98
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.07
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.06
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.36
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.78
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.49
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.62
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.26
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.90
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.38
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10262.16
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.54
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.71
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.28
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.22
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.57
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.50
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.53
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999980270
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.51
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999920714
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 246                :    0.9933
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.034
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:47.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99516443.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56258
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1219
 p-value of test no 12                 : 1 -  3.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334339
   j =  1                              :        599997562
   j =  2                              :             1219
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.44
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.27
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.28
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.41
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.53
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.60
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.00
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.77
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.12
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.42
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.35
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.16
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7299.63
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.24
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.70
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.51
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.29
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907848
   j =  2                              :            46067
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907730
   j =  2                              :            46132
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-4
 p-value of test no 109                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.92
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.91
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.61
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.56
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.54
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.08
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.87
 p-value of test no 135                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.87
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17608.64
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.74
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.64
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.49
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.97
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.02
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.44
 p-value of test no 152                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.94
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.64
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.22
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.64
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.16
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.35
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.39
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.07
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.37
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.03
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.65
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.81
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.98
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.41
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.37
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.53
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.85
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.06
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.84
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.79
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.37
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.17
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.40
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.47
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-4
 p-value of test no 180                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.42
 p-value of test no 183                :  7.8e-3
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.03
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.90
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
 p-value of test no 209                :    0.9946
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.85
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.25
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 217                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.57
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.00
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.10
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.03
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12033.47
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.82
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.91
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000154213
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.21
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000096403
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:02.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  3.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100532251.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56259
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     987
 p-value of test no 25                 :  2.2e-3
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.84
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.63
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.92
 p-value of test no 49                 :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.11
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.09
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.68
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.06
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.09
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.91
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.28
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6915.30
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.07
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.11
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.15
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.03
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.84
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908042
   j =  2                              :            45967
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908790
   j =  2                              :            45602
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 101                :    0.9923
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.10
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.26
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.74
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.90
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.42
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.65
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.59
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.83
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.10
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.57
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.72
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.91
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.10
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.52
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.80
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.53
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.88
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.89
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.52
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.50
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.58
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.47
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.65
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.64
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.58
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.85
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.61
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.31
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.79
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.00
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.77
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.39
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.06
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.48
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.37
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.54
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.32
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.68
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.70
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.66
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.94
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.96
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.78
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.75
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.89
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.66
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.34
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.13
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.30
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.34
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.78
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999877313
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.26
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999952286
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:02.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101548059.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56260
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7561
 p-value of test no 18                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 26                 :    0.9979
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    7.78
 p-value of test no 28                 :  1.5e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.31
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.49
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.62
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.16
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.20
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.22
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.60
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.69
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.50
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.97
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.45
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.89
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.66
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4918.21
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908595
   j =  2                              :            45695
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908124
   j =  2                              :            45929
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.60
 p-value of test no 115                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.74
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.30
 p-value of test no 121                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.46
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.60
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.82
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.25
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.31
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.46
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.73
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.74
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.00
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.66
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.51
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.73
 p-value of test no 155                :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.34
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.84
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.20
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.47
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.01
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.22
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.85
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.77
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.23
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.32
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.76
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.79
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.93
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.82
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.33
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.05
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.15
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.41
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.11
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.94
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.62
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.34
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.93
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.83
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.07
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 212                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9741.27
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.90
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.58
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3942.33
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.28
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.24
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.23
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.19
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999940790
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.40
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000043639
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:03.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NP, t = 5            1.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82018307.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56261
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1510
 p-value of test no 12                 :  5.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334630
   j =  1                              :        599996980
   j =  2                              :             1510
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9935
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.70
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.88
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.73
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.61
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.83
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.61
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.00
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.78
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.99
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.59
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.43
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.31
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.57
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907876
   j =  2                              :            46059
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.9e-3
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 92                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.33
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.55
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.73
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.09
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.23
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.04
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.44
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.43
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.96
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.10
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.66
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.43
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.32
 p-value of test no 150                :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.36
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.61
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.83
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.10
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.00
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.38
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.31
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.20
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.46
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.38
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.63
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.67
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.46
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.46
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.71
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.50
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.43
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.28
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.92
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.75
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.78
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.80
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.98
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.83
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.04
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.72
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.72
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.64
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.61
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.41
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.26
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.47
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.06
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.08
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000133159
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.64
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999995186
 
 Normal statistic for number of bits   :  -0.038
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:48.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           5.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83066883.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56262
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 29                 :    0.9965
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.02
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.42
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.99
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.27
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.67
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.77
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.44
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.19
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.51
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.14
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.97
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.06
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.38
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.39
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908325
   j =  2                              :            45833
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45618
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908772
   j =  2                              :            45602
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.70
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.52
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.57
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.17
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.77
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.25
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.13
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.31
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.26
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.90
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.59
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.42
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.50
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.05
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.88
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.15
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.65
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.30
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.39
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.61
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.90
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.44
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.54
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.22
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.93
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.59
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.28
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.59
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.97
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.92
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.52
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.78
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.54
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.73
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.45
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.76
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.14
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.56
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.23
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.24
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.83
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.00
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.12
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.83
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.71
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.94
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.83
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.13
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.87
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.11
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.08
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000185137
 
 Normal statistic for number of bits   :    1.46
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.50
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999837014
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:42.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84410371.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56263
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4199
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9936
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.59
 p-value of test no 50                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.23
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.80
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.49
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.51
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.45
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.52
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.21
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.03
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.57
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908361
   j =  2                              :            45812
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46143
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870143
   j =  1                              :        399907719
   j =  2                              :            46133
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 97                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.23
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.97
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.31
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.22
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.46
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.96
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.39
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.99
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.91
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.34
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.69
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.63
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.91
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.15
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.77
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.34
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.26
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.40
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.43
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.58
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.27
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.40
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.53
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.81
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.46
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.26
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.13
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.40
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.36
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.33
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.53
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.58
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.66
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.91
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.97
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.11
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.64
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.31
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.92
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.48
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.29
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.74
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.05
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.51
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.27
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.68
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.62
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.28
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.33
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.57
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.20
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.13
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999950882
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.18
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000098056
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:19.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85131267.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56264
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.94
 p-value of test no 45                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.31
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.24
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.58
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.60
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.77
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.68
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.84
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.16
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.02
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6925.75
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.14
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.94
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.13
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.20
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908756
   j =  2                              :            45616
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908079
   j =  2                              :            45953
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.15
 p-value of test no 119                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.56
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.64
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.55
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.55
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.93
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.04
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.70
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.13
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.03
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.48
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.53
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.90
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.31
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.49
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.85
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.52
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.70
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.15
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.14
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.84
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.24
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.52
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.32
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.13
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.97
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.43
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.49
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.06
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.60
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.15
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.27
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.87
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.43
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.20
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.47
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.93
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.16
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.06
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.33
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.28
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.13
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.43
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.26
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.62
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.12
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.33
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.52
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.00
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.11
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.05
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.75
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.98
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000089437
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.02
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000082315
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :   0.086
 p-value of test no 239                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.072
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:10.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86114307.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56265
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.04
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.09
 p-value of test no 41                 :  8.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.57
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.13
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.16
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.44
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.15
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.38
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.13
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.63
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.78
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.73
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.38
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.34
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.23
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907774
   j =  2                              :            46107
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907958
   j =  2                              :            46012
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.80
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.83
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.42
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 126                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   72.74
 p-value of test no 129                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.17
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.38
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.95
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.35
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.73
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.47
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.75
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.17
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.43
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.67
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.72
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.55
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.45
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.54
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.80
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.64
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.55
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.72
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.95
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.19
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.87
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.63
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.96
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.99
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.51
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.83
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.74
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.66
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.56
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9941
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.19
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.86
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.77
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.88
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.95
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.25
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.44
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4328.53
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.60
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12081.62
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.08
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.25
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000013498
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.79
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999879773
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.15
 p-value of test no 244                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:19.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87097347.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56266
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 16                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.12
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.69
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.61
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.59
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.53
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.42
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.86
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.71
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.23
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.85
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.35
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.11
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.60
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908113
   j =  2                              :            45936
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908029
   j =  2                              :            45981
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.7e-3
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.76
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.11
 p-value of test no 120                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.88
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.63
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.41
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.55
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.13
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.03
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.41
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.34
 p-value of test no 136                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.20
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17207.05
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.46
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.50
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.27
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.15
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.13
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.70
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.46
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.91
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.31
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.76
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.39
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.60
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.12
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.73
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.47
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.94
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.86
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.93
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.34
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.72
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.07
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.07
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.40
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.44
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.71
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.70
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.52
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.71
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.25
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.47
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.81
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.09
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.15
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.66
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.06
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.73
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.69
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.43
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.29
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.47
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000085249
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.27
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000175837
 
 Normal statistic for number of bits   :    1.39
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:20.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88145923.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56267
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 10                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 11                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.96
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    4.20
 p-value of test no 44                 :  7.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.06
 p-value of test no 46                 :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.59
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.14
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.85
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.47
 p-value of test no 51                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.41
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.55
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.64
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.59
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.62
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.32
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.27
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.24
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.31
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.06
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45419
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869419
   j =  1                              :        399909163
   j =  2                              :            45417
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908368
   j =  2                              :            45813
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.42
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.85
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.94
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.22
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.36
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 138                :  5.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    7.43
 p-value of test no 140                :  2.3e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   80.07
 p-value of test no 141                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.32
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.16
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.68
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.73
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.69
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.83
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.09
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.48
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.83
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.67
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.24
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.21
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.14
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.84
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.70
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.55
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.48
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.37
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.30
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.37
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.57
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.12
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.22
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.45
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.17
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.24
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.05
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.69
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.63
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.98
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.93
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.83
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.60
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.48
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9761.54
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.13
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.67
 p-value of test no 216                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.92
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.35
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.26
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.57
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.06
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.80
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.25
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000037825
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.35
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000013558
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9932
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.021
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:28.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89161731.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56268
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.69
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.25
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.63
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.45
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.57
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.65
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.53
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.43
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.79
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.73
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.58
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.78
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907782
   j =  2                              :            46100
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45558
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908887
   j =  2                              :            45552
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.21
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.41
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.70
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.39
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.09
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.24
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.17
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.02
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.18
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.04
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.98
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.82
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.89
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.50
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.44
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.69
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.54
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.44
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.83
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.52
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.01
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.63
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.91
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.96
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.03
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.17
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.97
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.94
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.41
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.04
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.76
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.23
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.13
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.12
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.18
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.72
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.05
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.73
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.09
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.60
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.26
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.90
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10231.76
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.025
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.23
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.27
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3937.09
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.55
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.60
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.49
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.96
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999990497
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.29
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000056086
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:39.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90177539.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56269
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.40
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.41
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.29
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.39
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.69
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.96
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.36
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.30
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.24
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.54
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.67
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.87
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4875.49
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908733
   j =  2                              :            45632
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908433
   j =  2                              :            45779
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 107                :  4.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.96
 p-value of test no 108                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.57
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.41
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.10
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.16
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.40
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.95
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.07
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17694.93
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.13
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.02
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.97
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.55
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.37
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.38
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.86
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.93
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.40
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.57
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.60
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.54
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.50
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.80
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.42
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.86
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.93
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.18
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.55
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.86
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.29
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.64
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.60
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.31
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.16
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.89
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.05
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.82
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.88
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.72
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.55
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.39
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.38
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.59
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.34
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.36
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.38
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.46
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.86
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.84
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.86
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.02
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000077320
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.05
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000002635
 
 Normal statistic for number of bits   :   0.021
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:36.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91193347.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56270
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    3.36
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     970
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.69
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.60
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.88
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.09
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.38
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.97
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.06
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.47
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.67
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.44
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.19
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.34
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5240.84
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45552
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908903
   j =  2                              :            45538
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907713
   j =  2                              :            46142
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-5
 p-value of test no 113                :    0.9901
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -4.20
 p-value of test no 118                : 1 -  1.4e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.31
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.17
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.47
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.45
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.29
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.61
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.89
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.85
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.86
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.14
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.79
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.37
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.39
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.86
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.90
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.81
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.88
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.89
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.73
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.49
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.60
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.09
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.10
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.30
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.16
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.11
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.29
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.96
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  308.77
 p-value of test no 169                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.32
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.82
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.81
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.51
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.52
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.91
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.12
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.41
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.66
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.10
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.15
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.22
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.58
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.01
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4339.98
 p-value of test no 228                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.89
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.86
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.97
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000096124
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.11
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999984467
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:01.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  58  AppearanceSpacings, r = 27     1 -  1.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92209155.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56271
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 12                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.13
 p-value of test no 30                 :    0.9994    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.52
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.24
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.10
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.70
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.77
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.20
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.89
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.10
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.22
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.43
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.57
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.38
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.58
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.90
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  162.63
 p-value of test no 67                 :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.01
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908638
   j =  2                              :            45675
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.16
 p-value of test no 119                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.04
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.97
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.15
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.68
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
 p-value of test no 126                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.66
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.91
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.02
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.43
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.34
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.13
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.27
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.11
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.06
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.98
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.98
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.57
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.49
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.74
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.86
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.97
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.36
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.63
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.94
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.37
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.72
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.98
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.96
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.52
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.33
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.36
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.15
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.07
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.46
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.97
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.98
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.29
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.10
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.85
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.30
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.97
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.49
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.54
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.51
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10325.26
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.98
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 225                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.89
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.88
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.80
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.28
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.97
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.25
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999893129
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.36
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999972776
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:17.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9994 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93257731.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56272
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4480
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.94
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.16
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.50
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.26
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.56
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.72
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.53
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.51
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.10
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.48
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.78
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.42
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.32
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.04
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.94
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908546
   j =  2                              :            45724
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907928
   j =  2                              :            46024
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.98
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.44
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.43
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.43
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.80
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.58
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.21
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.04
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.08
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17345.89
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.01
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.03
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.57
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.76
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.08
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.17
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.74
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.83
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.21
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.64
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.30
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.62
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.89
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.28
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.34
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.00
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.01
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.99
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.73
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.87
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.76
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.44
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.74
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.94
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.10
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.04
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.28
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.88
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.70
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.90
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.03
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 205                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.82
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.89
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.14
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.47
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 224                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5114.32
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.85
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.74
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.73
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.87
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.49
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000052516
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.95
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999949841
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:49.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94240771.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56273
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.02
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.07
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.25
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.47
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.61
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.93
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.04
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6727.28
 p-value of test no 57                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.85
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.82
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.13
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.88
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908541
   j =  2                              :            45728
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908364
   j =  2                              :            45812
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 92                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.21
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.97
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.43
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.61
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.72
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.26
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.78
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.02
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.10
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.92
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.56
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.86
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.46
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.86
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.37
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.99
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.13
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.73
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.25
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.18
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.08
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.24
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.10
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.30
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.46
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.14
 p-value of test no 161                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.39
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.14
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.56
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.26
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.67
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.71
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.09
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.23
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.37
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.25
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.75
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.10
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.10
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.16
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.43
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.97
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.80
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.28
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.15
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.06
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.05
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.25
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.92
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.69
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12041.45
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.99
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.89
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999993173
 
 Normal statistic for number of bits   :  -0.054
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.49
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999971168
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:06.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95256579.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56274
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997159
   j =  2                              :             1419
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 17                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.93
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.21
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.72
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.40
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.96
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.13
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.41
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.08
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.24
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.81
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.18
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.46
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.62
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.20
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908278
   j =  2                              :            45852
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908084
   j =  2                              :            45949
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-5
 p-value of test no 113                :    0.9924
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.88
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.91
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.41
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.08
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.04
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.13
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.82
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 131                :    0.9941
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.93
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.66
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.55
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.07
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.17
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.11
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.91
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.63
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.56
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.57
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.86
 p-value of test no 158                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.58
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.55
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.79
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.17
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.30
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.89
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.59
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.11
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.93
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.53
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.47
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.64
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.33
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.30
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.58
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.86
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.30
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.44
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.22
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.45
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.33
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.60
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.87
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.34
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.67
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.71
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.49
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.41
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.57
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999832892
 
 Normal statistic for number of bits   :   -1.32
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000077809
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.9913
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:03.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96337923.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56275
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9922
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.74
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.51
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.92
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.40
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.75
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.05
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.23
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.52
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.05
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.22
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.37
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.43
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.53
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908185
   j =  2                              :            45894
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908099
   j =  2                              :            45946
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.27
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.06
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.19
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.75
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.52
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.30
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.29
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.28
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.53
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.31
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.81
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.96
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.85
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.05
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.09
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.83
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.61
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.46
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.88
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.44
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.64
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.81
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.49
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.75
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.22
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.19
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.07
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.13
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.09
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.23
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.59
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.92
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.98
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.02
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.32
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.74
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.97
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.30
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.53
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.35
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.94
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.71
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.18
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.14
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.93
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.85
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.57
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.56
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.31
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999932816
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.14
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000087271
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:45.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97353731.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56276
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    3.44
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.32
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.74
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.88
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.07
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  184.38
 p-value of test no 54                 :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.09
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.78
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.10
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.84
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.14
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.60
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.68
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908281
   j =  2                              :            45852
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 93                 :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 95                 :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  1.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.50
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.69
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.89
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.14
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.19
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.08
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.34
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.90
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.43
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.63
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.29
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 143                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 144                :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17825.01
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.44
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.79
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.22
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.25
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.05
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.66
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.55
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.63
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.59
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.39
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.51
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.45
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.88
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.39
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.63
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.44
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.93
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.37
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.14
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.10
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.86
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.35
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.65
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.53
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.32
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.18
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.56
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.71
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.46
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.28
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.15
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.52
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.18
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.40
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.38
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.15
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.83
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.44
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.52
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11601.65
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.64
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000074800
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.68
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000025702
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 235                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.16
 p-value of test no 254                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:01.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98369539.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56277
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    5.39
 p-value of test no 24                 :  1.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     819
 p-value of test no 25                 :    0.9967
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.49
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.28
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.45
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.34
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.94
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.49
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.25
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6890.02
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.23
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.64
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.21
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.23
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.65
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908213
   j =  2                              :            45886
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908163
   j =  2                              :            45914
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 72                 :  5.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 74                 :  2.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9966
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.59
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.15
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.27
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.54
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.78
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.28
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.66
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.00
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17733.95
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.54
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.85
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.63
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.26
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.82
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.40
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.88
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.29
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.96
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.81
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.21
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.94
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.98
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.60
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.23
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.88
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.37
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.56
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.16
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.42
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.43
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.92
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.55
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.63
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.06
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.93
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.02
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.48
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.59
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.30
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.54
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.62
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.45
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.37
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.48
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.33
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.70
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.88
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.77
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.15
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.82
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000093730
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.65
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999967130
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:10.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99385347.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56278
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.95
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.14
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.76
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.50
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.36
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.01
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.92
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.58
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.31
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.19
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.18
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.09
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.46
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4878.14
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45438
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869438
   j =  1                              :        399909129
   j =  2                              :            45428
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907603
   j =  2                              :            46191
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-4
 p-value of test no 112                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 114                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.36
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.15
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.01
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.74
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.60
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.13
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.80
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.75
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.86
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.79
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.47
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.14
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.09
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.75
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.15
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.80
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.72
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.32
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.83
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.07
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.07
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.53
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.37
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.01
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.96
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.52
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.81
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.02
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.44
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.51
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.83
 p-value of test no 172                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.58
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.43
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.49
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.08
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.64
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.66
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.46
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.46
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10311.37
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.53
 p-value of test no 217                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.39
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.41
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.67
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.60
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.42
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11534.09
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.69
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000086413
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.41
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000103843
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.17
 p-value of test no 249                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:33.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100401155.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56279
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 9                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 12                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    3.98
 p-value of test no 30                 :  8.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.66
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.58
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.78
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.08
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.29
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.77
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.58
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.41
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.53
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.53
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.95
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.45
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.05
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.54
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.55
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908538
   j =  2                              :            45728
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908667
   j =  2                              :            45662
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 79                 :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9908
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 98                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.23
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.65
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.57
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.34
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.38
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.01
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.71
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.71
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.33
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.16
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.65
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.58
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.28
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.74
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.59
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.42
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.32
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.19
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.93
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.05
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.96
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.19
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.58
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.11
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.76
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.10
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.78
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.89
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.63
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.71
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.44
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.14
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.38
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.25
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5183.26
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.84
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.94
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.04
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.61
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.58
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.11
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.52
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.00
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.62
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.93
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.36
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.42
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.95
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.96
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.91
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000015688
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.77
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000052465
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.021
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:05.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101384195.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56280
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.33
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.09
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.13
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.46
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.14
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.57
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.41
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.55
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.28
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.58
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.59
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.58
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.11
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.08
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.11
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45532
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869532
   j =  1                              :        399908939
   j =  2                              :            45526
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908744
   j =  2                              :            45625
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.57
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.12
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.59
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.66
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.45
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.96
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.05
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.86
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 140                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  180.99
 p-value of test no 141                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17737.58
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.49
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.37
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.81
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.25
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.84
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.33
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.24
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.72
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.45
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.02
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.97
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.22
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.60
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.58
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.98
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   41.39
 p-value of test no 165                :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.60
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.79
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.33
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.48
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.46
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.92
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.56
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4685.22
 p-value of test no 173                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.14
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.64
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.77
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.02
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.32
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.62
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.46
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.35
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.16
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.05
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.68
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.12
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.45
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12170.61
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.01
 p-value of test no 231                :  3.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000041824
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.03
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999882923
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9962
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:43.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    0.9992 
  79  RandomWalk1 J (L=10000, r=15)   0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82051076.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56281
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997233
   j =  2                              :             1382
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.88
 p-value of test no 29                 :  3.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9942
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.41
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.36
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.08
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.11
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.16
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.78
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.06
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.30
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.00
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.01
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.45
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.55
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.00
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.06
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.74
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45370
 p-value of test no 70                 :    0.9913
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869370
   j =  1                              :        399909262
   j =  2                              :            45366
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45583
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869583
   j =  1                              :        399908835
   j =  2                              :            45581
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-3
 p-value of test no 86                 :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.15
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.46
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.71
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.67
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.52
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.83
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9970
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17380.86
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.90
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.15
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.41
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.53
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.98
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.47
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.37
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.88
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.87
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.75
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.84
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.56
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.42
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.26
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.82
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.10
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.25
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.16
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.02
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.66
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.38
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.60
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.78
 p-value of test no 172                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.32
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.80
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.45
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.03
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.68
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.83
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.60
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.43
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.43
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.96
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.20
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.42
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.17
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.56
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.83
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.86
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999906098
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.43
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000233086
 
 Normal statistic for number of bits   :    1.84
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:39.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82968580.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56282
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.62
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.75
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.91
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.47
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.71
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.16
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  183.71
 p-value of test no 54                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.76
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.73
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.00
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.43
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.20
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.07
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.04
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.36
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908613
   j =  2                              :            45686
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907941
   j =  2                              :            46025
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.18
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.52
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.64
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.45
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.57
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.44
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.52
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.52
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.71
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.54
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.99
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.62
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.10
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.95
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.42
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.40
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.82
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.21
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.14
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.10
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.23
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.20
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.68
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.27
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.88
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.95
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.51
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.28
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.95
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5197.64
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.96
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.06
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.02
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.02
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.26
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.75
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.77
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.49
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.11
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.86
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.29
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.29
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.17
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.28
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.59
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.71
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.49
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.21
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.87
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.64
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000107458
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.23
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000009397
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:50.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84049928.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56283
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7543
 p-value of test no 20                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.05
 p-value of test no 40                 :  9.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.07
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.32
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.64
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.49
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.01
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.78
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.87
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.88
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45642
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908720
   j =  2                              :            45634
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908669
   j =  2                              :            45658
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.16
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.18
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.30
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.29
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.35
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.48
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.04
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.14
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.16
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.74
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.49
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.57
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.63
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.10
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.07
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.63
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.67
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.67
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.35
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.27
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.46
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.62
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.91
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.21
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.33
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.24
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.67
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.68
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.33
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  306.88
 p-value of test no 166                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.29
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.79
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.68
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.87
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.30
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.10
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.06
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.29
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.77
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.77
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.95
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.29
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.73
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.69
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.22
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.39
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.27
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.91
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.12
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.16
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11579.00
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.90
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999890195
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.80
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999976286
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:43.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85000200.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56284
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.40
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.25
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.39
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.34
 p-value of test no 51                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.56
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.92
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.80
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.80
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.67
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.16
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.00
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.50
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.17
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4944.12
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46294
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907417
   j =  2                              :            46284
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908777
   j =  2                              :            45607
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.49
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.05
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.95
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.19
 p-value of test no 122                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.41
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.13
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 126                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.57
 p-value of test no 129                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.56
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.22
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.76
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.75
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 142                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17023.40
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.42
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.17
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.83
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.90
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.31
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.66
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.27
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.30
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.18
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.34
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.24
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.99
 p-value of test no 160                :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.40
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.60
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.93
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.20
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.02
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.36
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.57
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.80
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.10
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.57
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.23
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.00
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.49
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.45
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.64
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.43
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.37
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.73
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.82
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.14
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.38
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.66
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.66
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4334.87
 p-value of test no 227                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.89
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.16
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.61
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.58
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999994676
 
 Normal statistic for number of bits   :  -0.042
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.22
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999890702
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:19.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86048776.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56285
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5532
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.64
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.29
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.37
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.95
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.06
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.12
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.20
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.29
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.78
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.25
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.11
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.88
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.45
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.62
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.53
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908171
   j =  2                              :            45910
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  8.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.78
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.42
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.40
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.01
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.30
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.93
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.77
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.95
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.84
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.61
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.97
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.71
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.51
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.90
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.86
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.01
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.87
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.85
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.91
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.57
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.87
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.30
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.87
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.93
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.80
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.04
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.73
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.40
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.14
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.31
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.93
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.77
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.04
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.22
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.47
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.46
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.08
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.32
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.37
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.54
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.90
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.44
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.62
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.04
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5053.23
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.64
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.95
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.72
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.31
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.68
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.80
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999864473
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.41
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000019405
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:12.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87064584.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56286
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7525
 p-value of test no 21                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.96
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.72
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.45
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.10
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.53
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.90
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.83
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.85
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.85
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 60                 :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.85
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.68
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.67
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.23
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.71
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908741
   j =  2                              :            45625
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46357
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870357
   j =  1                              :        399907289
   j =  2                              :            46351
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.76
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.17
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.18
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.19
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.78
 p-value of test no 124                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.74
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.86
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.92
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.46
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.01
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.77
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.32
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.50
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.64
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.52
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.33
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.62
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.59
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.89
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.98
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.52
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.17
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.69
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.29
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.71
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.98
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.67
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.46
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.11
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.58
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.81
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.39
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.01
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.85
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.04
 p-value of test no 174                :    0.9955
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.20
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.04
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.36
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.61
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.96
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.40
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.68
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.27
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.65
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.09
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.15
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.08
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.48
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.86
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000169027
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.75
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000112027
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:11.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88047624.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56287
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    3.94
 p-value of test no 45                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.40
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.99
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.71
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.82
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.35
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.21
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.15
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.65
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.98
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.42
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.04
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.09
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.62
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5211.51
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908156
   j =  2                              :            45919
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908440
   j =  2                              :            45774
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.75
 p-value of test no 85                 :  3.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.98e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.65
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.38
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.58
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.55
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.59
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.73
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.35
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.32
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.87
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17527.34
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.22
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.96
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.03
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.26
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.03
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.62
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.06
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.28
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.26
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.11
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.59
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.08
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.51
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.93
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.56
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.76
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.51
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.60
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.71
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.40
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.69
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.55
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.78
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.81
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.85
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.19
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.65
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.97
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.39
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.48
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.33
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 206                :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.82
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.12
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.18
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.76
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.41
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.83
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.97
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11543.69
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.58
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.57
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000081454
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.35
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000000751
 
 Normal statistic for number of bits   : 5.94e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.046
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:59.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89063432.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56288
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.60
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.63
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.78
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.70
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.87
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.00
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.71
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  289.37
 p-value of test no 54                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  370.63
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.98
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6838.66
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.04
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.21
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.67
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.72
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908717
   j =  2                              :            45637
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908379
   j =  2                              :            45809
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.56
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.35
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.40
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.17
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.41
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.78
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.47
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.39
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.89
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.83
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.15
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.86
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.55
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.14
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.78
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.97
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.63
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.49
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.26
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.40
 p-value of test no 160                :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.97
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.19
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.09
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.51
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.94
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.21
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.23
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.84
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.31
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.93
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.79
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.97
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.06
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.52
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.26
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.65
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.44
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.93
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.03
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.38
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.67
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.52
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.68
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4373.94
 p-value of test no 227                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.64
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.49
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.39
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.99
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000033727
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.53
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000011389
 
 Normal statistic for number of bits   :   0.090
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 236                :  1.0e-2
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:09.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90112008.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56289
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    4.04
 p-value of test no 27                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.24
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.93
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.57
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.63
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.07
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.66
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.59
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.81
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.98
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.32
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.81
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.75
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46267
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870267
   j =  1                              :        399907473
   j =  2                              :            46253
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907820
   j =  2                              :            46087
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.88
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.71
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.12
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.65
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.17
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.78
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.79
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.41
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.35
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-3
 p-value of test no 138                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.78
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17664.38
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.58
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.19
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.66
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.58
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.35
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.06
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.52
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.60
 p-value of test no 156                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.07
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.50
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.34
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.03
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.27
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.84
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.30
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.80
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.38
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.60
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.24
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.51
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.07
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.73
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.08
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.82
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.75
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.70
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.04
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.12
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    2.25
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.54
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.06
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.65
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.22
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.09
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.07
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5117.57
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3969.70
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.91
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.37
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.86
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.31
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999904142
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.05
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000046282
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:47.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91160584.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56290
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 7                  :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.32
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.96
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.02
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.09
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.93
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.67
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.28
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.26
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.98
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.17
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5207.35
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908187
   j =  2                              :            45905
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.83
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.34
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.82
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.20
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.28
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.32
 p-value of test no 124                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.56
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.85
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.06
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.10
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.22
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.21
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.75
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.94
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.36
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.15
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.50
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.74
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.89
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.38
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.53
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.84
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.50
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.97
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.94
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.79
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.63
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.90
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.71
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.60
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.46
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.43
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.69
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.14
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.88
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.21
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.79
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.65
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.33
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 181                :  9.8e-5    *****
 
 Anderson-Darling statistic = A2       :    7.05
 p-value of test no 182                :  3.4e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.20
 p-value of test no 183                :  7.0e-4    *****
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.81
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.71
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.53
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.78
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.43
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5034.35
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.36
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.80
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.77
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.20
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.65
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000035272
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.16
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999996068
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.59
 p-value of test no 243                :    0.9952
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 250                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:35.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  82  LempelZiv, r = 0                7.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92176392.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56291
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4479
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7097
 p-value of test no 20                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.19
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.55
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.64
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.68
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.64
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1332.43
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.20
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.07
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.14
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.83
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.23
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.91
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45485
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869485
   j =  1                              :        399909032
   j =  2                              :            45481
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908085
   j =  2                              :            45956
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-3
 p-value of test no 80                 :    0.9981
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.36
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.30
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.10
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.98
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.73
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.79
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.03
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.25
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.68
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.56
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.35
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17445.10
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.46
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.57
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.60
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.03
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.97
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.85
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.03
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.98
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.34
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.50
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.69
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.11
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.92
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.48
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.79
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.57
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.43
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.00
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.40
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  459.22
 p-value of test no 169                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.02
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.46
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.38
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.03
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.47
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.14
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.16
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.22
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.24
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10229.34
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.98
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.66
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.89
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.59
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.63
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.48
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.63
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.92
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999902207
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.38
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999864779
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    2.19
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:33.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93192200.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56292
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.29
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.93
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    5.41
 p-value of test no 42                 :  1.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    3.67
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.76
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.94
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.29
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.38
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.69
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.55
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  505.22
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.14
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7272.57
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.53
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.59
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.25
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4896.16
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908305
   j =  2                              :            45846
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907704
   j =  2                              :            46145
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 93                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 99                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-6
 p-value of test no 113                :    0.9974
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.51
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.40
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.11
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.58
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.22
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.85
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.79
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.84
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.70
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17461.95
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.80
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.54
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.54
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.48
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.32
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.37
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.22
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.42
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.73
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.46
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.07
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.49
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.21
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.58
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.24
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.70
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.10
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.67
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.64
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.52
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.67
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.34
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.26
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.65
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.72
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.02
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.64
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.11
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.55
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.78
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.50
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.48
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.99
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.03
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.32
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.11
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.06
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.36
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.07
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.34
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.31
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999934229
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.23
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999883004
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.13
 p-value of test no 249                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 250                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:46.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94208008.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56293
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1534
 p-value of test no 12                 :  3.4e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334654
   j =  1                              :        599996932
   j =  2                              :             1534
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5299
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 38                 :    0.9941
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.78
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.97
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   91.99
 p-value of test no 50                 :  9.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.93
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.82
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.22
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.33
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.27
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.60
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.66
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.63
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.94
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   73.61
 p-value of test no 67                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.23
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907999
   j =  2                              :            45996
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908254
   j =  2                              :            45870
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.14
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.02
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.19
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.24
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.99
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.10
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.41
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.82
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.50
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.77
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.50
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.99
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.24
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.92
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.46
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.21
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.87
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.49
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.34
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.10
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.37
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.19
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.50
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.04
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.96
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.97
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.87
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.67
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.85
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.89
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.84
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.48
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.89
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.17
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.23
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.69
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.27
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.34
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    2.94
 p-value of test no 189                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.38
 p-value of test no 196                :    0.9945
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.25
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-4
 p-value of test no 205                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.09
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10217.03
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.91
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.17
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.15
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.81
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.31
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11682.37
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.70
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.32
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999970955
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.58
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999971363
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 251                :    0.9942
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:00.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           3.4e-6
  30  CouponCollector, r = 0          9.7e-4
  41  Permutation, t = 5              0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95223816.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56294
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 3                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9918
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     538
 p-value of test no 31                 :    0.9946
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.67
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.08
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.03
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.07
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.19
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.66
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.51
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.47
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.36
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.19
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.41
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.13
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.45
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.90
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.60
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46049
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907910
   j =  2                              :            46033
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908391
   j =  2                              :            45800
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
 p-value of test no 104                :    0.9959
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.13
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.97
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.15
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.63
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.17
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.04
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.22
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.71
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.05
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.23
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.77
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.02
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.14
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.06
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.18
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.87
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.87
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.55
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.34
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.28
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.20
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.01
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.07
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.83
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.24
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.52
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.67
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.45
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.67
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.55
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.31
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.81
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.64
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.26
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.09
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.88
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.92
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.32
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.77
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.00
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.56
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.71
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.96
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.90
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.09
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.29
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.13
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.29
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.07
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.01
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000127480
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.19
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000058660
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    2.67
 p-value of test no 254                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:29.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96305160.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56295
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.00
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.88
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.27
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.72
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.14
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.11
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.39
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.95
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.23
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.38
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.72
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.30
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.12
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908470
   j =  2                              :            45756
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908361
   j =  2                              :            45815
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.49
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.65
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.94
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.36
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.77
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.70
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.61
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.04
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.69
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 143                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17740.43
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.11
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.91
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.24
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.95
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.86
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.64
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.70
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.16
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.74
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.25
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.28
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.35
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.21
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.73
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.58
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.48
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.37
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.44
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.48
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.42
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.54
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.79
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.83
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.60
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.04
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.46
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.16
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.12
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.95
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.87
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.68
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.42
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.10
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.26
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.13
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.33
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.14
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.56
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.93
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999911339
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.68
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999998276
 
 Normal statistic for number of bits   :  -0.014
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.22
 p-value of test no 239                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    2.03
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:41.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97320968.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56296
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 6                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    4.73
 p-value of test no 30                 :  3.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     682
 p-value of test no 31                 :  5.5e-4    *****
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.71
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9952
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.89
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.39
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.10
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.73
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.52
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.70
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.43
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.68
 p-value of test no 58                 :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.88
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.07
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.44
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.38
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.71
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908461
   j =  2                              :            45765
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908036
   j =  2                              :            45973
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 77                 :    0.9947
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.78
 p-value of test no 116                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.39
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.50
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.18
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.53
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.57
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.88
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.52
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.94
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.85
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.02
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.32
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.48
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.49
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.69
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.99
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.50
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.53
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.91
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.75
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.59
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.92
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.21
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.83
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.80
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.30
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.05
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.73
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.95
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.79
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.84
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.25
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.05
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.15
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.75
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 188                :    0.03
 
 Sample variance                       :    2.04
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.41
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.72
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.00
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.80
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.11
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.22
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.13
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.58
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.29
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.29
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.53
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.87
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999903836
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.82
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999914675
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    2.25
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:49.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        5.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98336776.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56297
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 10                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.79
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.72
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.97
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.64
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.10
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.58
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.44
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.26
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.47
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.86
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.51
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.85
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.81
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.47
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5222.62
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46414
 p-value of test no 70                 :  6.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870414
   j =  1                              :        399907177
   j =  2                              :            46404
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908372
   j =  2                              :            45808
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.96
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.62
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.67
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.82
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.88
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.76
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.40
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.12
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.24
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17151.91
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.88
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.18
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.21
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.91
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.70
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.53
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.97
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.39
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.40
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.59
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.88
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.47
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.11
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.81
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.56
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.16
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.11
 p-value of test no 164                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.05
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.58
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.41
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.70
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.38
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.87
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.83
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.59
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.68
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.80
 p-value of test no 174                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.81
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.36
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.11
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.21
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.86
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.44
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.27
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.03
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
 p-value of test no 219                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5137.68
 p-value of test no 222                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.87
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.07
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.40
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.79
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.63
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.27
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999861311
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.57
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999829304
 
 Normal statistic for number of bits   :   -1.35
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.22e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-4
 p-value of test no 245                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.52
 p-value of test no 248                :  5.8e-3
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:43.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99352584.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56298
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.85
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.03
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.69
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.58
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.01
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.69
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.23
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.11
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 58                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   53.50
 p-value of test no 61                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.63
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.26
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.36
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.66
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908080
   j =  2                              :            45951
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908230
   j =  2                              :            45882
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 107                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.00
 p-value of test no 115                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.59
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.84
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.58
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.10
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.37
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.45
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-3
 p-value of test no 126                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.17
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.51
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.26
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.41
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.84
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17610.47
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.06
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.43
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.05
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.88
 p-value of test no 150                :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.17
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.85
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.43
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.80
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.77
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.49
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.63
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.82
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.48
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.06
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.17
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.80
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.20
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.21
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.82
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.87
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.86
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.68
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.60
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.94
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.04
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.32
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.91
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.06
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.88
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.16
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.67
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.46
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.91
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.68
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.89
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.70
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.53
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11512.96
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.18
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.69
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999871964
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.04
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999865601
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.74
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:15.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100368392.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56299
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.52
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.39
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.13
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.79
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.01
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.89
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.83
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.51
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.59
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.03
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.81
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.75
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.06
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.79
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.83
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907578
   j =  2                              :            46205
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908058
   j =  2                              :            45962
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.73
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.04
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.12
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.90
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.81
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.61
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.35
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   16.65
 p-value of test no 135                :  8.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.10
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.86
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.96
 p-value of test no 148                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.37
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.08
 p-value of test no 150                :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.95
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.50
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.20
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.08
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.28
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.97
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.45
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.15
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.80
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.79
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.41
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.94
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.62
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.53
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.44
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5254.32
 p-value of test no 168                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.05
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.00
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.97
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.99
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.85
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.67
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.87
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.79
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    2.18
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.55
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.47
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.76
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.26
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.00
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.50
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.77
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.19
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.14
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.84
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.11
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.76
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999917873
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.23
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000007684
 
 Normal statistic for number of bits   :   0.061
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:56.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        8.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101351432.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56300
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.40
 p-value of test no 22                 :  6.6e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    3.69
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.67
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.40
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.02
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.35
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.16
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.97
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.44
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.08
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.82
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.29
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.99
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.68
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4938.00
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907563
   j =  2                              :            46214
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45981
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908043
   j =  2                              :            45971
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
 p-value of test no 72                 :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.70
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.48
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.95
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.06
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.71
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.64
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.54
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.48
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17525.41
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.59
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.56
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.74
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.33
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.26
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.36
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.79
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.64
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.23
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.34
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.11
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.46
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.62
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.82
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.52
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.44
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.60
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.31
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.42
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.66
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.28
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.04
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.02
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.72
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.77
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.53
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.78
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.89
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.11
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.42
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.75
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.46
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.85
 p-value of test no 217                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.30
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.16
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.75
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.38
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12051.64
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.96
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.19
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999980606
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.77
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000048442
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:52.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            6.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82083845.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56301
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.27
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.48
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.17
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.88
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.97
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.86
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.59
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.51
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.92
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.94
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.71
 p-value of test no 66                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.37
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.68
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908559
   j =  2                              :            45716
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908270
   j =  2                              :            45859
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.22
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.03
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.22
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.58
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.38
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.20
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.82
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.84
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.100
 p-value of test no 135                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 140                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.89
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.89
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.42
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.36
 p-value of test no 147                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.19
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.47
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.36
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.34
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.41
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.62
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.04
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.01
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.44
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.52
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.78
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.78
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.65
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.64
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.74
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.78
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.04
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.30
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.47
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.80
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.31
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.17
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.04
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.39
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.46
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.54
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.50
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.21
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.02
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.43
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.38
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.24
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.54
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.33
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.35
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12146.15
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.73
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.92
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000095827
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.61
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000032908
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:12.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83623941.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56302
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 15                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.67
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.09
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.05
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.31
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.87
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.05
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.94
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.25
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.24
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.37
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5262.10
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908449
   j =  2                              :            45768
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908384
   j =  2                              :            45805
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.01
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.97
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.65
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.70
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.86
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.22
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.35
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.47
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.13
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17546.26
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.89
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.39
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.04
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.36
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.32
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.92
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.84
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.61
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.94
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.39
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.83
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.90
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.60
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.89
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.24
 p-value of test no 161                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.73
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.44
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.68
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.38
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.17
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.31
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.94
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.28
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.87
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.18
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.52
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5327.29
 p-value of test no 173                :  6.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.01
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.22
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.81
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.87
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.12
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.68
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.77
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.70
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.07
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.61
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.67
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.84
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.35
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.71
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.17
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.12
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000042169
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.09
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999881798
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:03.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   6.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84508677.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56303
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    4.29
 p-value of test no 27                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.22
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.24
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.63
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.50
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.02
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.47
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.25
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7080.63
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.81
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.41
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.23
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.60
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908096
   j =  2                              :            45946
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908254
   j =  2                              :            45873
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 97                 :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    4.10
 p-value of test no 99                 :  8.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.86
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.03
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.31
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.15
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.17
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.24
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.88
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.64
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.83
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.41
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17322.81
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.06
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.53
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.24
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.33
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.29
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.96
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.02
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.82
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.79
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.90
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.35
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.39
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.86
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.48
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.27
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.80
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.53
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.35
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.79
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.48
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.95
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.87
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.75
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.04
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.15
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.63
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.31
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.75
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.31
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.46
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.68
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9760.57
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.99
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.79
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.13
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.17
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.70
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.99
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.67
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   28.88
 p-value of test no 231                :    0.9980
 
 
 -----------------------------------------------
 Total number of bits:  8000085588
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.70
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999969023
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:41.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85327877.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56304
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7559
 p-value of test no 20                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.42
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.83
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.82
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.56
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.34
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.59
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.55
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.95
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.69
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.35
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.98
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.73
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.07
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.19
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907704
   j =  2                              :            46145
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908307
   j =  2                              :            45842
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.96
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.92
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.53
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.29
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.02
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.65
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.54
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.03
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.59
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.51
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.97
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.16
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.52
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.56
 p-value of test no 148                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.76
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.94
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.89
 p-value of test no 152                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.36
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.47
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.76
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.60
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.05
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.74
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.85
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.29
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.38
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.63
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.46
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.95
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5231.39
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.16
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.46
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.45
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.12
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.43
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.10
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.65
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.96
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.91
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.20
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.24
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.85
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.08
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.91
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.96
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.03
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.70
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.16
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.87
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.37
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999992306
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.66
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000095953
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:29.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86540293.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56305
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.72
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.59
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.22
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.15
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.32
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.01
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6920.33
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.38
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.14
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.31
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.72
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908032
   j =  2                              :            45975
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908173
   j =  2                              :            45909
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
 p-value of test no 98                 :    0.9973
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-4
 p-value of test no 110                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.55
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.93
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.50
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.50
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.07
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.67
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.35
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.19
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.52
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.32
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.25
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.74
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.20
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.88
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.15
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.80
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.30
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.68
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.61
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.68
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.31
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.49
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.35
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.27
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.71
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.84
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.06
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.75
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.83
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.25
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.87
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.77
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.43
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.32
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.11
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.29
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.50
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.72
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.32
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.33
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.62
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.76
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.44
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.57
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.43
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.21
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.99
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4278.16
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.00
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.10
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.63
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.45
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999956930
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.60
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000104044
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
 p-value of test no 250                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    5.13
 p-value of test no 252                :  2.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.27
 p-value of test no 253                :  5.4e-4    *****
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:36.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  106  AutoCor, d=3, r=27              5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87556101.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56306
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.91
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.92
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.90
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.70
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.27
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.23
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.94
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.46
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.05
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.74
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.35
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.52
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.76
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45574
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869574
   j =  1                              :        399908853
   j =  2                              :            45572
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908481
   j =  2                              :            45755
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.19
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.75
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.38
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.45
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.22
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.54
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.68
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.84
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.88
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.25
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.96
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.50
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.06
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.26
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.65
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.29
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.35
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.84
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.91
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.62
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.59
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.44
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.68
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.23
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.10
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.61
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.61
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.91
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.40
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.88
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.57
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.38
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.03
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.74
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.18
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.94
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.79
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.91
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.59
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.21
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.94
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.94
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.41
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.15
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.50
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.56
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.19
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.47
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.38
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.43
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.94
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.22
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000008995
 
 Normal statistic for number of bits   :   0.071
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.38
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999835499
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 253                :  7.0e-3
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:49.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88408088.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56307
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.56
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.17
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.80
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.36
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.48
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.40
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.16
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.07
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.26
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.55
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.39
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5238.62
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907822
   j =  2                              :            46086
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45703
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908599
   j =  2                              :            45693
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.43
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.81
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.38
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.90
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.91
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.23
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.81
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.54
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.29
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.58
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.59
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.78
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.66
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.65
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.96
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.72
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.43
 p-value of test no 157                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.81
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.65
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.66
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.40
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.97
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.90
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.96
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.52
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.92
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.77
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.01
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.01
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.53
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.47
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.50
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.24
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.27
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.51
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.09
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.61
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.97
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.11
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.57
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.41
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.65
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.08
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.18
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.64
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.15
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.75
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.90
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.95
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.52
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000167242
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.79
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000041080
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.90
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:32.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89325592.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56308
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5532
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7611
 p-value of test no 20                 :  3.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7515
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 40                 :    0.9960
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.40
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.59
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.95
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.28
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.60
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.97
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.20
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.68
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.35
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.99
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.53
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.98
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907824
   j =  2                              :            46085
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908230
   j =  2                              :            45873
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-4
 p-value of test no 79                 :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-5
 p-value of test no 113                :    0.9900
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.53
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.85
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.25
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.81
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.59
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.09
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.31
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.86
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.78
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 139                :    0.9954
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.94
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.93
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.03
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.13
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.12
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.15
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.67
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.46
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.22
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.57
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.76
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.69
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.13
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.12
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.00
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.26
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.63
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.70
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.51
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.75
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.19
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.16
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.66
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.69
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.00
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.14
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.80
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.16
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.56
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.21
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.93
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.27
 p-value of test no 203                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.28
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.26
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.64
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.90
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.36
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.11
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.47
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.12
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.38
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.39
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999874910
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.33
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000043432
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:58.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        3.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90308632.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56309
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5257
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.05
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.53
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.11
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.23
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.52
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.43
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.78
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.49
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.07
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45414
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869414
   j =  1                              :        399909172
   j =  2                              :            45414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907978
   j =  2                              :            46002
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-4
 p-value of test no 109                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -2.48e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.15
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.42
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.60
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.05
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.46
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.48
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.56
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.48
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.00
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.66
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.28
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.20
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.97
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.35
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.20
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.26
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.57
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.58
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.87
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.31
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.42
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.70
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.57
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.17
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.07
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.87
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.77
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.38
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.68
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.36
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.49
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.32
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.70
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.76
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.07
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.51
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.61
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.72
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.45
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.03
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.73
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.58
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.60
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.64
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 208                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10248.98
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.38
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.03
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.97
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.09
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.12
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.52
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.18
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.84
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000128131
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.84
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999872381
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:58.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91324440.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56310
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.99
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.58
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.28
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.34
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.78
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.63
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.16
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.62
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.98
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.59
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.88
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.67
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.05
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.52
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908617
   j =  2                              :            45681
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907982
   j =  2                              :            46003
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 80                 :  2.3e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 103                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.18
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.08
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.64
 p-value of test no 122                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.80
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.70
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.59
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.89
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.13
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.28
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.67
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.97
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.26
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.55
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.30
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.39
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.10
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.15
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.22
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.75
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.41
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.90
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.15
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.66
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.02
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.22
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.79
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.20
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.05
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.35
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.61
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.90
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.33
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.82
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.26
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.67
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.13
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.56
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 197                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.53
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.28
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.63
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.10
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.94
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.10
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.49
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.38
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.82
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11595.85
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.32
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000025924
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.15
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000045151
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.069
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:12.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92438552.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56311
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 3                  :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     827
 p-value of test no 25                 :    0.9927
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.56
 p-value of test no 47                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.10
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.41
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.70
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.74
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.85
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.78
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.54
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 59                 :    0.9951
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.45
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.37
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.50
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.84
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5222.57
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907925
   j =  2                              :            46033
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908370
   j =  2                              :            45812
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 118                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.87
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.46
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.44
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.56
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.09
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 126                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.89
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.09
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.28
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.83
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.09
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.85
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.17
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.40
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.65
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.07
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.68
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.81
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.81
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.10
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.86
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  588.79
 p-value of test no 163                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.22
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.31
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.65
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.22
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.35
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.07
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.21
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.67
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.71
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.19
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.60
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.72
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.18
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.33
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.19
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.10
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.02
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.41
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.56
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.34
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.99
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.49
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.93
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999917234
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000044761
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.86
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:25.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93552664.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56312
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 11                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.98
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.24
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   41.67
 p-value of test no 49                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.92
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.00
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.04
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.66
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.77
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.96
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.62
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.39
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.92
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.93
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.61
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907910
   j =  2                              :            46036
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907764
   j =  2                              :            46112
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 105                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.12
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.72
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.30
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.22
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.85
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.51
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.093
 p-value of test no 134                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.28
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17618.81
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.44
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.22
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.19
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.53
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.62
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.38
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.81
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.05
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.21
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.86
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.29
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.08
 p-value of test no 158                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.86
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.42
 p-value of test no 160                :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.10
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.47
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.63
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.62
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.79
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.98
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.98
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.88
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.01
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.65
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.75
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.36
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.47
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.04
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.72
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.54e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.78
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.38
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.92
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.59
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.72
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.79
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.36
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.01
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.93
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.16
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.01
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000011242
 
 Normal statistic for number of bits   :   0.089
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.40
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999985382
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    2.29
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:11.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94535704.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56313
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9940
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.75
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.70
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.41
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.14
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.72
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.65
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.56
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.27
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.03
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.51
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.05
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.85
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.70
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.95
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.95
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908630
   j =  2                              :            45682
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45459
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869459
   j =  1                              :        399909084
   j =  2                              :            45455
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.41
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.61
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.98
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.62
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.17
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.00
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.38
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.51
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.63
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.79
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.52
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.11
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.12
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.32
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.88
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.16
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.44
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.14
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.07
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.27
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.38
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.76
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.87
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.85
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.43
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.95
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.89
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.47
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.52
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.70
 p-value of test no 167                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.33
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.23
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.22
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.38
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.63
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.50
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.76
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.42
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.59
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 186                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 187                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.71
 p-value of test no 188                :  3.4e-3
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.30
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.74
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.61
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.38
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 213                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.72
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.49
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.37
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4275.28
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.31
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.84
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.94
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.75
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999916901
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.57
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000000829
 
 Normal statistic for number of bits   : 6.55e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:53.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95977496.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56314
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.42
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.97
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.27
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.94
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.72
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.58
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.31
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.94
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.09
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.22
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1342.46
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.75
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.74
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.67
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.80
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5228.29
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908439
   j =  2                              :            45776
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907842
   j =  2                              :            46073
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 81                 :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 95                 :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9970
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 118                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.96
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.15
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.95
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.22
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.76
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 130                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.96
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.64
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.90
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.70
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.14
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.35
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.56
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.64
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.13
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.76
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.46
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.27
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.65
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.84
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.76
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.06
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.09
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.69
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.76
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.17
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.54
 p-value of test no 166                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.55
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5184.82
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.84
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.52
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.95
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.52
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.51
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.93
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.51
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.97
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.32
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.26
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.96
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.31
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.03
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.41
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.77
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.55
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.87
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.60
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.15
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.10
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000028513
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.46
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999993713
 
 Normal statistic for number of bits   :  -0.050
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -1.92e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:02.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96960536.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56315
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.20
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.05
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.14
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.00
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.25
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.67
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.32
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.64
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.63
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.22
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.25
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.74
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.53
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.92
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908323
   j =  2                              :            45834
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907891
   j =  2                              :            46053
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.04
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.28
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.97
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.32
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.30
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.00
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.77
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.75
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.55
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.39
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.14
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.17
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.85
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.32
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.88
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.78
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.30
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.32
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.13
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.55
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.62
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.33
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.12
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.50
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.67
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.89
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.19
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.76
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.17
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.68
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.28
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.77
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.12
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.98
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.30
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.58
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.83
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.10
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.97
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.04
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.07
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.43
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.42
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.78
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.45
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.57
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.82
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.69
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.07
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.41
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.61
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000088105
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.25
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000004921
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 235                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 237                :  9.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.68
 p-value of test no 238                :  3.6e-3
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    2.50
 p-value of test no 249                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 253                :    0.94
 
 Sample variance                       :    2.13
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:43.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97976344.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56316
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.53
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.35
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.81
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.99
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.74
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.75
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.42
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.26
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.66
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.51
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.09
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.02
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.34
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4904.04
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907562
   j =  2                              :            46216
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907662
   j =  2                              :            46163
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.95
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.20
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.19
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.29
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.33
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.34
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.19
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.37
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.41
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.32
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.31
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.89
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.42
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.97
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.49
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.32
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.22
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.38
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.26
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.62
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.00
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.48
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.18
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.96
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.02
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.62
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.21
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.31
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.10
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.08
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.75
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.11
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.08
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.54
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.44
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.70
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.78
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.58
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.54
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.65
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.19
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.94
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.98
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.91
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.35
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.81
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.78
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.09
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.08
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.97
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000068041
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.90
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999928871
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.23
 p-value of test no 244                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:28.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98893848.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56317
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.43
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.20
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.92
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.86
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.91
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.72
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.70
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.76
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.47
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.43
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   57.05
 p-value of test no 61                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.52
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.51
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.10
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.47
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45514
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869514
   j =  1                              :        399908975
   j =  2                              :            45508
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46303
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870303
   j =  1                              :        399907398
   j =  2                              :            46295
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.08
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.35
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.36
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.96
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.99
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.75
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.02
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.01
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.65
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.02
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.35
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.72
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.13
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.56
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.93
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.99
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.64
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.17
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.65
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.35
 p-value of test no 159                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.84
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.23
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.09
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.53
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.00
 p-value of test no 164                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.49
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.44
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.11
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.55
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.23
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.53
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.83
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.63
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.40
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.15
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.53
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.02
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.92
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.82
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.11
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
 p-value of test no 213                :    0.9965
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9654.61
 p-value of test no 215                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.29
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.74
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.85
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.43
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.50
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.17
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.98
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999814403
 
 Normal statistic for number of bits   :   -1.47
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.42
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999919583
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.14e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:15.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99844120.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56318
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 12                 :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9928
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.73
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    3.57
 p-value of test no 48                 :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.05
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.15
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.74
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.04
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.85
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.02
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1288.53
 p-value of test no 56                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.92
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.45
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.34
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.51
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.96
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907910
   j =  2                              :            46039
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9944
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.055
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.45
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.65
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.04
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.91
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.93
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.81
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.48
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.62
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.72
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.40
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.57
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.36
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.45
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.78
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.17
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.47
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.88
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.89
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.18
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.15
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.13
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.40
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.77
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.72
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.54
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.74
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.39
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.50
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.91
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.87
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.93
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.85
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.70
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.15
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.51
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.72
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.13
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.53
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.39
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.31
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.91
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.76
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.46
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.03
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.59
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.20
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11485.14
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.05
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999864602
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.64
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999959936
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:20.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           7.8e-4
  28  SimpPoker, r = 0                0.9999 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100761624.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56319
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7105
 p-value of test no 20                 :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.00
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.53
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.22
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.25
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.41
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.65
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.09
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.23
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.86
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.12
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.66
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.82
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.42
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908203
   j =  2                              :            45891
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907879
   j =  2                              :            46056
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.76
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.46
 p-value of test no 120                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.82
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.74
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.73
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.45
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.01
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.64
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.70
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.32
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17528.68
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.78
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.19
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.12
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.50
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.51
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.64
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.03
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.81
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.05
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.31
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.63
 p-value of test no 159                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.84
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.93
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.59
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.22
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.78
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.74
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.09
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.62
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.74
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.19
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.13
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.05
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.08
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.45
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.32
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 188                :    0.9939
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.07
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.63
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.35
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.59
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.86
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.90
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.62
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3939.80
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.04
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.40
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.00
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999949655
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.60
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999865238
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
 p-value of test no 235                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.33
 p-value of test no 238                :  1.0e-2
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9937
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 1.70e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:56.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101777432.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56320
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997247
   j =  2                              :             1375
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.57
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    3.33
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     256
 p-value of test no 37                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.12
 p-value of test no 39                 :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    3.55
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.04
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.51
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.11
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.21
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.67
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.04
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.05
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7381.70
 p-value of test no 57                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.49
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.94
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.22
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.28
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.63
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908602
   j =  2                              :            45696
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908438
   j =  2                              :            45769
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 100                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.54e-4
 p-value of test no 110                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 111                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.19
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.15
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.20
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.61
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.87
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.90
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.31
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.55
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.82
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.79
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.13
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.65
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.59
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.56
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.55
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.47
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.69
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.20
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.65
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.16
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.58
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.90
 p-value of test no 156                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.14
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.31
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.81
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.32
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.77
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.39
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.21
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.41
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  299.03
 p-value of test no 166                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.60
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.91
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.27
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.91
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.51
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.50
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.76
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.56
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.66
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.41
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.43
 p-value of test no 198                :    0.9938
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.49
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.04
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.09
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.74
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.43
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.34
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.17
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.90
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.65
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.17
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.92
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999957026
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.38
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000050365
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:20.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2S, t = 9         0.9998 
  78  RandomWalk1 H (L=10000, r=0)    0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82116614.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56321
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7130
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.33
 p-value of test no 47                 :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.10
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.83
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.26
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.11
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.06
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.43
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.66
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.45
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.46
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.85
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.24
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.00
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5142.82
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907991
   j =  2                              :            45997
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907961
   j =  2                              :            46015
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-4
 p-value of test no 109                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.56
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.58
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.23
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.16
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.71
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.25
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.94
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.45
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.89
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17510.93
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.00
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.26
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.47
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.70
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.77
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.99
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.43
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.22
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.42
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.51
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.39
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   92.63
 p-value of test no 159                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.89
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.85
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.34
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.36
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.93
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.68
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.70
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.21
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.23
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.45
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.14
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.96
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.80
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.46
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.67
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.86
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.16
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.84
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.56
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.12
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9732.30
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.70
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.47
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.72
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.91
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.83
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11516.84
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.73
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.00
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000106273
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.62
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999875585
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:04.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               0.9999 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83460114.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56322
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    3.40
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.45
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.51
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.28
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.20
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.12
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.86
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.75
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.89
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.91
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.44
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.24
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.48
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.99
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.52
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908253
   j =  2                              :            45866
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908220
   j =  2                              :            45887
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.91
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.45
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.17
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.50
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.08
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.60
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.27
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.34
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.51
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.63
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.42
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.54
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.77
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.97
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.27
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.22
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.55
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.97
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.31
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.26
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.65
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.99
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.65
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.60
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.27
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.00
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.74
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.11
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.53
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.28
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.16
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.65
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.03
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.90
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.53
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.53
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.47
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.88
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.48
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 199                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.21
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.06
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10310.27
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.59
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5095.98
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.75
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.22
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.53
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.85
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.98
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.21
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999792764
 
 Normal statistic for number of bits   :   -1.64
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.91
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000132880
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 241                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:07.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84213778.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56323
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.30
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.58
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.90
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.09
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.21
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.39
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.45
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.08
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.21
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.84
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.06
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.12
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.48
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.83
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908354
   j =  2                              :            45823
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45500
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869500
   j =  1                              :        399909003
   j =  2                              :            45494
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-4
 p-value of test no 113                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 114                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.27
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.25
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.80
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.30
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.21
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.55
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.46
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.98
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.32
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.77
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.21
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.61
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.00
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.32
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.29
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.15
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.56
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.09
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.06
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.88
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.90
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.75
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.85
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.19
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.89
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.92
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.25
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.26
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.88
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.36
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.35
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.65
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.90
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.11
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.57
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.93
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.89
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.49
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.31
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.71
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.38
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.38
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.26
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.61
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.37
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.18
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.50
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.20
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.61
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.23
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.23
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000051895
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.94
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000202690
 
 Normal statistic for number of bits   :    1.60
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:52.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85164050.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56324
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.17
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.54
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.97
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.44
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.04
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.50
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.83
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.25
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.01
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.68
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.11
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.17
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908085
   j =  2                              :            45956
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908120
   j =  2                              :            45934
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.61
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.95
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.27
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.88
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.68
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.97
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.64
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 139                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.74
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 144                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.98
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.64
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.04
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.49
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.57
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.73
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.74
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.95
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.23
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.10
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.61
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.28
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.78
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.97
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.14
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.47
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.91
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.54
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.71
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  312.04
 p-value of test no 172                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.70
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.09
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.98
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.00
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.55
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.86
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.92
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.07
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.38
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.32
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.10
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.61
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.92
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.60
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.34
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.24
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000092404
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.80
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999995315
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:25.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86343694.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56325
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 7                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.83
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.22
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.24
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.60
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.85
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.64
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.84
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.01
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.25
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.74
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.47
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.06
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.14
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.73
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.70
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908189
   j =  2                              :            45895
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907870
   j =  2                              :            46059
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 98                 :    0.9932
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.21
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.92
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.13
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.63
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.88
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.16
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.60
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.65
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.18
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.037
 p-value of test no 135                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.88
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17308.02
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.52
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.34
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.40
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.81
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.90
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.94
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.08
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.11
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.25
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.71
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.81
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.78
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.57
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.59
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.65
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.44
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  206.58
 p-value of test no 164                :  9.1e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.27
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.43
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.82
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.11
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.65
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.65
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.35
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.95
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.86
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.02
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.48
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.53
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.02
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.57
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.62
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.30
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.96
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 212                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 214                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9580.93
 p-value of test no 215                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.45
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.88
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.12
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.78
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11395.83
 p-value of test no 229                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.03
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.03
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999957173
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.30
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000087001
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:06.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    9.1e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87359502.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56326
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.47
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.30
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.32
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.60
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.75
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.78
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.11
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.38
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.86
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.46
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.36
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.34
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.73
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.62
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45590
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869590
   j =  1                              :        399908825
   j =  2                              :            45580
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908497
   j =  2                              :            45750
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-6
 p-value of test no 110                :    0.9987
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.64
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.67
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.03
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.25
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.68
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.83
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.74
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.02
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.27
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.30
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.88
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.76
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.73
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.63
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.08
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.85
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.45
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.63
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.40
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.95
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.60
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.29
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.55
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.54
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.66
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.75
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.55
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.74
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.11
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.84
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.00
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.26
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.25
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.97
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.60
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.17
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.90
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.83
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.00
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.66
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.99
 p-value of test no 198                :  7.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.88
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.39
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.68
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.78
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.97
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.06
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.55
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.05
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.57
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.77
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999767282
 
 Normal statistic for number of bits   :   -1.84
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999888992
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:04.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88211470.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56327
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 10                 :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.56
 p-value of test no 23                 :  1.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.72
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.53
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.76
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.15
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.33
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.88
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.66
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.19
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.20
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.23
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.83
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.20
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.57
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.15
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.04
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907673
   j =  2                              :            46156
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907894
   j =  2                              :            46047
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.87
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.58
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.94
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.47
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.60
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.14
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.51
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.31
 p-value of test no 136                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.55
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17621.27
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.86
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.52
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.09
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.95
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.56
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.00
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.08
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.34
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.31
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.36
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.33
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.15
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.82
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.11
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.24
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.40
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.46
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.55
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.62
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.61
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  312.86
 p-value of test no 169                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.93
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.44
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.40
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.42
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.70
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.56
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 181                :  7.4e-4    *****
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.89
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.69
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 201                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 202                :  8.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.65
 p-value of test no 203                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.20
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.15
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.56
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.03
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.45
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.88
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.10
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.69
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.00
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.23
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000005362
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.50
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999934403
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:21.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89260046.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56328
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7110
 p-value of test no 18                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.03
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.85
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.77
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.83
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.64
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.94
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.67
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.92
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.90
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.23
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6917.55
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.15
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.23
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.06
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.08
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908212
   j =  2                              :            45891
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908224
   j =  2                              :            45885
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 108                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.49
 p-value of test no 116                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.85
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.90
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.63
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.92
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.07
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.13
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.14
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.43
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
 p-value of test no 130                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.99
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.94
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.71
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.12
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.67
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.45
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.90
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.22
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.62
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.76
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.44
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.49
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.36
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.15
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.06
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.66
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.37
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.66
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.51
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  577.71
 p-value of test no 163                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  204.24
 p-value of test no 164                :  1.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.62
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.29
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.01
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.87
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.35
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.19
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.65
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.60
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.83
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.31
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.16
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.72
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.00
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.10
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.52
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.31
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.33
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.10
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.98
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.19
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.69
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.74
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.24
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.19
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999966845
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000055549
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:05.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9998 
  77  RandomWalk1 R (L=1000, r=20)    1.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90341390.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56329
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.27
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.83
 p-value of test no 49                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.41
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.85
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.33
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.29
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.61
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.81
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.84
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.25
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.11
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.96
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908576
   j =  2                              :            45709
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.36e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.45
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.56
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.94
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.75
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.70
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.06
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.34
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.56
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 138                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
 p-value of test no 139                :    0.9975
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 140                :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   87.44
 p-value of test no 141                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.84
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.84
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.68
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.32
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.46
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.10
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.42
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.11
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.10
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.88
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.08
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.36
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.40
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.42
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.52
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.87
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.42
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.50
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.09
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.88
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.19
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.94
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.60
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.29
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.05
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.35
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.55
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.14
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.94
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.04
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.02
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.04
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.22
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.70
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.01
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.54
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.72
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.06
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.90
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.73
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.27
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.39
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000022495
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.07
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999931901
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 252                :    0.9997    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.66e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:03.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91389966.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56330
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.38
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.82
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.00
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.38
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.79
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.84
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.00
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.10
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.33
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.67
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.20
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.39
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.36
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908170
   j =  2                              :            45912
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908150
   j =  2                              :            45919
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.77
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.63
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.50
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.42
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.54
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.54
 p-value of test no 134                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.76
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.36
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.19
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.24
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.91
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.41
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.41
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.06
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.29
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.88
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.32
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.74
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.58
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   89.20
 p-value of test no 159                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.00
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.45
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.24
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.47
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.44
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.71
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.31
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.47
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.10
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.82
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.84
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.88
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.28
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.28
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.12
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.00
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.90
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.27
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.77
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.40
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.42
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.38
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3922.05
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.25
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.23
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.98
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.16
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000096487
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.76
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000059239
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:41.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92373006.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56331
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 4                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 28                 :    0.9965
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9935
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.82
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.70
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.60
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.93
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.48
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  504.99
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.61
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.47
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.74
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.30
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.76
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.56
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.80
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907975
   j =  2                              :            46011
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907910
   j =  2                              :            46042
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.72
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.32
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.85
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.75
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.93
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.20
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.00
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.20
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.80
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.21
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.83
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.44
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.81
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.96
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.63
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.20
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.69
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.76
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.99
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.29
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.07
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.73
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.35
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.20
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.21
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.04
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.90
 p-value of test no 164                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.67
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.47
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.75
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.29
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.70
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.54
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.99
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.05
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.51
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.05
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.24
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.16
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.84
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.67
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.77
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.81
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.37
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.92
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.06
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.08
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.05
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.10
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.76
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.75
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999993842
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.27
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000006769
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:38.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93356046.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56332
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    5.90
 p-value of test no 36                 :  1.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     349
 p-value of test no 37                 :  3.1e-3
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.05
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.06
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.39
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.26
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.05
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.16
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.99
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.26
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.50
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.62
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.80
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.94
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.26
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.10
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.31
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.54
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908184
   j =  2                              :            45902
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908555
   j =  2                              :            45721
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-6
 p-value of test no 110                :    0.9971
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.17
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.94
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.99
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.32
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.23
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.31
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.50
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.95
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.19
 p-value of test no 135                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.39
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.47
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.97
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.35
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.88
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.58
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.71
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.18
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.77
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.74
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.43
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.63
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.82
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.35
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.12
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.57
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.72
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.43
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.43
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.97
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.75
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.52
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.66
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.73
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.65
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.87
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.13
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.13
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.94
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.63
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.90
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.28
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.05
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.18
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.63
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.39
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.15
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 218                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.71
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.96
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.92
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.06
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.37
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.71
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.32
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000132190
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.68
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999891452
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:50.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94371854.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56333
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.89
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.53
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.64
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.85
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.02
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.76
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.95
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7199.02
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.40
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.81
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.16
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.76
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908140
   j =  2                              :            45924
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908779
   j =  2                              :            45603
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.94
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.25
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.84
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.59
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.63
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.85
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.08
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.22
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 142                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    6.51
 p-value of test no 144                :  6.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16780.47
 p-value of test no 145                :    0.9998    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.97
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.09
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.16
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.03
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.88
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.35
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.62
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.92
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.70
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.10
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.41
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.36
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.57
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.55
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.38
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.26
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.96
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.72
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.98
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.64
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.85
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.73
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.14
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.46
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.44
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.07
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.26
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.49
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.88
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.89
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.95
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.87
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.67
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.73
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.87
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.24
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.33
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.17
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.12
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.87
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.22
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.91
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999890000
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.84
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999932351
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:00.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  73  GCD                             0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95387662.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56334
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.01
 p-value of test no 35                 :  3.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9931
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9916
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.31
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.40
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.57
 p-value of test no 53                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.82
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.39
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.52
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.76
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.42
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.39
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.22
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.79
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46435
 p-value of test no 70                 :  4.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870435
   j =  1                              :        399907134
   j =  2                              :            46427
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908758
   j =  2                              :            45615
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
 p-value of test no 107                :    0.9964
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.41
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.27
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.73
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.76
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.28
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 127                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.76
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.46
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.20
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.50
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.38
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.05
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.29
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.60
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.50
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.16
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.23
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.70
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.35
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.90
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.49
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.79
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.86
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.35
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.29
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.35
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.36
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.92
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.36
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.56
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.45
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.79
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.55
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.02
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.97
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.97
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.38
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.06
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.10
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.14
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.59
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.83
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.26
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.36
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.19
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.84
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.74
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.16
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.78
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.29
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.92
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.13
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000048211
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.47
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000060901
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:30.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96370702.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56335
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.46
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.94
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.27
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.08
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.81
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.92
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.57
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.69
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.42
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.21
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.63
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.29
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.36
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.20
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908254
   j =  2                              :            45870
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908072
   j =  2                              :            45964
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.71
 p-value of test no 115                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.92
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.31
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.67
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.21
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.75
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.03
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.80
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.22
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.50
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.27
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.67
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.59
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.27
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.74
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.06
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.07
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.26
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.80
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.27
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.02
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.89
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.49
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.66
 p-value of test no 160                :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.13
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.95
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.44
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.90
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.79
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.98
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.02
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.90
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.99
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.36
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.98
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.15
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.96
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.73
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.28
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.00
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.57
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.49
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.46
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.70
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.07
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.98
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.63
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.14
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.76
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.65
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.66
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999972044
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.35
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000101587
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:57.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97386510.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56336
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 12                 :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4170
 p-value of test no 14                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    3.05
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    3.64
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.68
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.23
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.22
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.43
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.70
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.90
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.01
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.77
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.21
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.85
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.70
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.28
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908416
   j =  2                              :            45789
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908652
   j =  2                              :            45668
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.49
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.83
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.55
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.28
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.32
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.46
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.06
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.08
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.21
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.34
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.22
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.00
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.79
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.66
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.99
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.14
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.94
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.60
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.78
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.60
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.52
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.29
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.20
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.67
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.95
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.74
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.76
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.95
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.44
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.11
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.28
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.90
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.61
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.90
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.89
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.60
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.75
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.76
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.83
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.48
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.86
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.16
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.45
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.98
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.27
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.75
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.94
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.48
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.63
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999996335
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.43
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000099670
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:52.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98402318.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56337
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4139
 p-value of test no 17                 :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.98
 p-value of test no 35                 :  9.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.87
 p-value of test no 47                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.08
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.70
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.38
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.28
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.95
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.37
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.22
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.95
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.16
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.03
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.33
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.22
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.82
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.00
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907968
   j =  2                              :            46013
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908606
   j =  2                              :            45691
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.04
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.49
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.22
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.62
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.79
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.05
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.08
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.77
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17324.61
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.76
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.09
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.47
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.05
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.01
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.98
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.59
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.51
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.37
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.31
 p-value of test no 157                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.09
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.17
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.82
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.44
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.55
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.17
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.68
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.71
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.59
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.93
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.67
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.43
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.96
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.41
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.95
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.05
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.35
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.74
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.13
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.00
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    2.47
 p-value of test no 184                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.80
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.49
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.85
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.75
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.60
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.97
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4730.88
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.64
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.13
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.98
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.03
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.42
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000009226
 
 Normal statistic for number of bits   :   0.073
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.60
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999968783
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:57.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99418126.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56338
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.06
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.79
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.30
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.79
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.34
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.61
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.77
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.22
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.64
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.93
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.31
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.93
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.86
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.97
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.90
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.79
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.50
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908667
   j =  2                              :            45659
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907752
   j =  2                              :            46121
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9980
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 106                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    5.46
 p-value of test no 108                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 3.27e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.51
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.15
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.20
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.40
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.65
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.00
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.51
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17007.30
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.25
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.46
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.85
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.56
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.28
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.01
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.70
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.12
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.20
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.37
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.16
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.80
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.02
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.48
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.77
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.14
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.80
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.11
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.03
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.69
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.28
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.97
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.30
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.40
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.35
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.52
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.13
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.62
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.31
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.60
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.28
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.16
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.18
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 212                :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9684.21
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.71
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.04
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.51
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.97
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.20
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.46
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.82
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000153478
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.96
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000088147
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:38.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100433934.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56339
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7111
 p-value of test no 20                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.82
 p-value of test no 23                 :  3.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.49
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.70
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.18
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.28
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.84
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.50
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.21
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.70
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.06
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.09
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.97
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.19
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.49
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46210
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870210
   j =  1                              :        399907586
   j =  2                              :            46198
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907971
   j =  2                              :            46007
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.055
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.82
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.76
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.19
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.37
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.75
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.15
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.63
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.95
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.79
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.97
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.92
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.11
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.64
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.58
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.40
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.12
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.53
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.90
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.19
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.80
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.84
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.99
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.10
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.57
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.40
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.11
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.86
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.38
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.69
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.78
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.57
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.68
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.75
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.67
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.16
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.80
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.78
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.61
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.96
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.79
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.65
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.98
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.70
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.33
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.82
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12059.15
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.33
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000052807
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.94
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000112198
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:44.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101449742.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56340
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.46
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9903
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.78
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.29
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.61
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.75
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.46
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.97
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.22
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.81
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.91
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.19
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.28
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.22
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.58
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.57
 p-value of test no 67                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.13
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908641
   j =  2                              :            45672
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907804
   j =  2                              :            46092
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.35
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.40
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.08
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.53
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.16
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.86
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.55
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.13
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.05
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.07
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 143                :    0.9953
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17030.23
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.07
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.47
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.12
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.10
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.63
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.61
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.54
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.65
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.72
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.20
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.32
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.94
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.13
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.92
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.87
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.72
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.12
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.21
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.41
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.66
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.15
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.39
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.28
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.14
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5203.63
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.38
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.45
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.09
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.24
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.82
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.23
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.36
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.07
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.35
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.74
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.88
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.31
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.47
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.01
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.61
 p-value of test no 231                :  4.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999905015
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.93
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999899255
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:11.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82149383.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56341
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 5                  :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 12                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    3.23
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.62
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.78
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.20
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.45
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.50
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.34
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.00
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.91
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.61
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.14
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.95
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.14
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5199.82
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908044
   j =  2                              :            45972
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46099
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870099
   j =  1                              :        399907806
   j =  2                              :            46091
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 101                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.73
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.08
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.91
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.49
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.13
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.90
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.62
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.35
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.65
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.93
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.27
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.04
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.39
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.36
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.03
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.09
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.60
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.99
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.81
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.73
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.79
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.11
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.09
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.46
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.72
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.83
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.01
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.24
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.83
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.11
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.40
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.13
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.50
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.63
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.51
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.60
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.47
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.31
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.08
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.36
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5053.66
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.25
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4332.44
 p-value of test no 227                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3930.01
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.29
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.93
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.19
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000094876
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.75
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999853589
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:43.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83263495.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56342
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.08
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.00
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.09
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.09
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.27
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.57
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.51
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.80
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.25
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.52
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.44
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.06
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46118
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907769
   j =  2                              :            46108
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908607
   j =  2                              :            45689
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 74                 :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 103                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 104                :    0.9957
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 105                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-3
 p-value of test no 107                :    0.9978
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.48
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.38
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.63
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.31
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.70
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.82
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.93
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 128                :  5.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.46
 p-value of test no 129                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.68
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17325.43
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.02
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.44
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.10
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.02
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.06
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.64
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.99
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.05
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.21
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.41
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.67
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.07
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.75
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.16
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.00
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.44
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.24
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.61
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.14
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.03
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.59
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.24
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.55
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.22
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.45
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.56
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.62
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.76
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.13
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.94
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.34
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.28e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.87
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5087.99
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.02
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.18
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.84
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.80
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.16
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999857183
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.31
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999850850
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:05.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84475911.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56343
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 22                 :    0.9988
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    3.57
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.26
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.00
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.01
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.34
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.24
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.00
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.71
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.83
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.08
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 60                 :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.25
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.77
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.63
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4879.42
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908517
   j =  2                              :            45737
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907762
   j =  2                              :            46113
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.79
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.95
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.94
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.64
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.03
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.00
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.33
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.16
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.27
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.93
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.51
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.90
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.07
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.55
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.04
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.11
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.50
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.16
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.83
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.08
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.77
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.95
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.63
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.76
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.40
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.87
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.49
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.58
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.79
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.90
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.36
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.28
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.20
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.94
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.93
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.78
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.85
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.46
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.71
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.18
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.67
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.54
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.86
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.26
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.74
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.41
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.50
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.75
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.48
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.70
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.30
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.38
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000014566
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.81
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000059044
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:37.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85295111.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56344
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5547
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7078
 p-value of test no 19                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.74
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.75
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.93
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.32
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.76
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.41
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.29
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.14
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.52
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.63
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.69
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.30
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908576
   j =  2                              :            45706
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908143
   j =  2                              :            45924
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.92e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.24
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.51
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.04
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.23
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.39
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.05
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.79
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.40
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.47
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17686.08
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.75
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.75
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.99
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.36
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.23
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.25
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.21
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.99
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.93
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.70
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.64
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.80
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.12
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.87
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.27
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.86
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.12
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.19
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.66
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.25
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.31
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.02
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.59
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.24
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.61
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.51
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.65
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.66
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.14
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.03
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.09
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.86
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.78
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
 p-value of test no 205                :    0.9965
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.53
 p-value of test no 207                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.67
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.33
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.65
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.93
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.88
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.61
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.86
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11567.02
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.58
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999970901
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.30
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000044950
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 236                :  1.0e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 237                :  7.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.28
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:46.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86507527.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56345
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.85
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9930
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.69
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.03
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.70
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.11
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.63
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.56
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.20
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.95
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.66
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.00
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.95
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.14
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.53
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.88
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.95
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907918
   j =  2                              :            46032
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907901
   j =  2                              :            46045
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 74                 :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  1.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.57
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.26
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.11
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.59
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.17
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.41
 p-value of test no 124                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.97
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.93
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.62
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.43
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.31
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.20
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.98
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.16
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.63
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.40
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.73
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.18
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.85
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.70
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.42
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.50
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.94
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.01
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.85
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.03
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.86
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.30
 p-value of test no 164                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.10
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.94
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.44
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.59
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.45
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.00
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.35
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.30
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.25
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.63
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.47
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.91
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.64
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.01
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.44
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.21
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.94
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4698.68
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.44
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.73
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.25
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.16
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.33
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.74
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999980648
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.81
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000074470
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:59.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87916551.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56346
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.12
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9917
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.79
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.21
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.88
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.35
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.59
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.63
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.82
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.74
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.24
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.05
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.68
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.02
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.99
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.11
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.11
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907924
   j =  2                              :            46032
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907943
   j =  2                              :            46021
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 83                 :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.03
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.66
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.12
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.76
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.60
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.55
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.86
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.20
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.02
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.21
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.19
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.04
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.14
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.15
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.70
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.21
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.29
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.27
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.10
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.82
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.05
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  188.01
 p-value of test no 159                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.31
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.91
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  603.40
 p-value of test no 163                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.17
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.17
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.23
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.28
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.06
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.09
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.99
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.03
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.02
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.78
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.45
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.67
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.86
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.03
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.28
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.77
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.35
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.42
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.71
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.78
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.00
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.25
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3918.71
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.62
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.26
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.74
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000041689
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.96
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000088915
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:23.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88866823.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56347
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1206
 p-value of test no 12                 : 1 -  6.7e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334326
   j =  1                              :        599997588
   j =  2                              :             1206
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    3.44
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.09
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.47
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.34
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.48
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.50
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.51
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.31
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.33
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7268.16
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.51
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.48
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.61
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.88
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908760
   j =  2                              :            45617
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908033
   j =  2                              :            45979
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9923
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.51
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.05
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.93
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.71
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.31
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.05
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
 p-value of test no 142                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17675.92
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.57
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.08
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.67
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.85
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.43
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.68
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.29
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.78
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.14
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.69
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.08
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.67
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.22
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.91
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.03
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.43
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.79
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.62
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.07
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.92
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.31
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.51
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.71
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.67
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.29
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.29
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.38
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.30
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.96
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.91
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.54
 p-value of test no 196                :  5.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.25
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.21
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.49
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.67
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.44
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.17
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.13
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4244.52
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.61
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12105.34
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.11
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999934079
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.71
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000019264
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:32.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  6.7e-6
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89817095.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56348
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4492
 p-value of test no 14                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     258
 p-value of test no 37                 :    0.9928
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.82
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.02
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.04
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.11
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.51
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.15
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.70
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.16
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.57
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.96
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.02
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.48
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.66
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.72
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.83
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908132
   j =  2                              :            45925
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45422
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869422
   j =  1                              :        399909159
   j =  2                              :            45416
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.21
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.18
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.56
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.19
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.44
 p-value of test no 124                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.82
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.68
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.15
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.22
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.55
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.30
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.57
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.38
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.12
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.24
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.41
 p-value of test no 151                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.05
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.11
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.74
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.16
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.29
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.05
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.11
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.53
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.74
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.66
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.62
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.32
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.66
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.15
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.44
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.01
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.87
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.32
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.27
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4752.41
 p-value of test no 173                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.64
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.65
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.48
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.58
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.76
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.88
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.52
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.35
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4681.79
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.87
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.10
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.00
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.19
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.21
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.11
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999910226
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.62
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000037963
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.78e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:12.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90832903.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56349
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 9                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.55
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.64
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.47
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.40
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.85
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.99
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.23
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.65
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.02
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.68
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.38
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.08
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.24
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.44
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.06
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.59
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.29
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.57
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908659
   j =  2                              :            45666
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908088
   j =  2                              :            45953
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 98                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.82
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.77
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.97
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.57
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.42
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.06
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.49
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.25
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.80
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.42
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.20
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.06
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.56
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.55
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.43
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.15
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.30
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.08
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.64
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.53
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.98
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.16
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.28
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.76
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.11
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.60
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.44
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.83
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.24
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.54
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.69
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.99
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.22
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.49
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.73
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.90
 p-value of test no 172                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.24
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.05
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.29
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.77
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.77
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.37
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.56
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 214                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.32
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.84e-4
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.51
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.86
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.06
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.41
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.37
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11402.15
 p-value of test no 230                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.89
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999824897
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.61
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000060763
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    2.39
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:38.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91914247.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56350
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7141
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     539
 p-value of test no 31                 :    0.9939
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.10
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.98
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.43
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.11
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.85
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.98
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.37
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.02
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.33
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7181.94
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.91
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.98
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.47
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.86
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.68
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908582
   j =  2                              :            45700
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908517
   j =  2                              :            45734
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.77
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.90
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.02
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.84
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.87
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.43
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.71
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.90
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.51
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17869.60
 p-value of test no 145                :  9.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.19
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.98
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.09
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.89
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.05
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.62
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.71
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.17
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.37
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.02
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.32
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.49
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.94
 p-value of test no 160                :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.69
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.05
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.84
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.07
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.40
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.97
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.55
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.04
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.43
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.46
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.25
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.76
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.39
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.47
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.83
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.89
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.79
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.10
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.03
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.97
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.17
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5036.16
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.54
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.14
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12166.09
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.98
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.54
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999919748
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.09
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000009910
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:48.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92962837.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56351
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.87
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    6.27
 p-value of test no 32                 :  7.4e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.07
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.58
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.52
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.70
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.37
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.42
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.19
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.44
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.05
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.15
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.17
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5234.57
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46145
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907710
   j =  2                              :            46145
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908235
   j =  2                              :            45875
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 79                 :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 115                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.01
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.08
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.24
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.71
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.33
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.92
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.20
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.49
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.21
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.34
 p-value of test no 136                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.54
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.44
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.47
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.74
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.47
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.14
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.00
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.68
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.69
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.59
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.72
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.78
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.37
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.09
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.44
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.53
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.42
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.62
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.41
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.95
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.15
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.45
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.38
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.39
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.92
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.54
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.28
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.94
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.70
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.59
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.48
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.27
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.89
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.26
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.91
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.65
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.57
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.47
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.24
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.45
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.27
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.30
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.84
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.53
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.56
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.22
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999961553
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.61
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000054103
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9968
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.54e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.091
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:40.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          7.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93978645.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56352
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.04
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.55
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.55
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.61
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.59
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.12
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.28
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.65
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.73
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.70
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.72
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.12
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908718
   j =  2                              :            45635
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45703
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908597
   j =  2                              :            45697
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-5
 p-value of test no 110                :    0.9957
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.90
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.39
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.60
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.18
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.81
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.49
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.37
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17195.69
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.27
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.00
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.78
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.70
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.01
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.95
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.55
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.10
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.24
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  575.23
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.77
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.36
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.99
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.87
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.64
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.35
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.99
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.57
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.94
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.62
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.84
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.76
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.27
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.57
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.11
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.22
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.86
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    2.57
 p-value of test no 189                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.03
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.79
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.36
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.65
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.72
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.18
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.45
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.76
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.34
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.99
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.32
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000126859
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.97
 p-value of test no 233                :    0.9926
 
 
 -----------------------------------------------
 Total number of bits:  7999873017
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.40
 p-value of test no 243                :    0.9918
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:04.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94928917.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56353
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 6                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 11                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 12                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9927
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.87
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.28
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.18
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.08
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.94
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.39
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.16
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.09
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.60
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6904.72
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.40
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.79
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.14
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.73
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908199
   j =  2                              :            45893
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46305
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870305
   j =  1                              :        399907394
   j =  2                              :            46297
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.89
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.02
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.59
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.44
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.74
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.99
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.48
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17162.92
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.27
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.62
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.21
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.71
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.75
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.44
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.25
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.83
 p-value of test no 156                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.61
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.29
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.52
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.66
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.41
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.36
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.76
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.96
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.68
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.48
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.10
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.90
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.89
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.65
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.28
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.44
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4722.06
 p-value of test no 173                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.73
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.08
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.00
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.74
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.89
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 209                :    0.9948
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9664.35
 p-value of test no 211                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.20
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 217                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.30
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.34
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.20
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.06
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.57
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.38
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.87
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999990812
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.35
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999842429
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.24
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.053
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:13.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96043029.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56354
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.25
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.10
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.19
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.16
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.58
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.62
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.29
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.68
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.32
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.41
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.38
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.56
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.76
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.98
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.86
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908281
   j =  2                              :            45852
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908198
   j =  2                              :            45895
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 83                 :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.13
 p-value of test no 118                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.28
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.83
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.82
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.74
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.74
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.67
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.61
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.37
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.76
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.50
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.74
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.77
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.17
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.98
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.68
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.51
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.46
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.25
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.26
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.72
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.09
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.72
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.68
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.45
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.62
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.13
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.09
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.64
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.32
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.55
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.32
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.02
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.89
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.77
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.89
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.57
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.97
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.19
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.33
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.46
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.26
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.08
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.29
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.85
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.93
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10230.71
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.29
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.60e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.33
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.69
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.93
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.15
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.27
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.78
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.36
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000198547
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.62
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999895520
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:16.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  58  AppearanceSpacings, r = 27      0.9991 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97124373.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56355
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.70
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.61
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.28
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.57
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.15
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.11
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.26
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.81
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.50
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.43
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.27
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.85
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.41
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.02
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.72
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908494
   j =  2                              :            45750
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908584
   j =  2                              :            45705
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.81
 p-value of test no 119                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.09
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.75
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.52
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.46
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.00
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.88
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.46
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.62
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.97
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.88
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.69
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.19
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   67.31
 p-value of test no 152                :  8.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.63
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.64
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.39
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.98
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.78
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.56
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.43
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.66
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.88
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.10
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.26
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.71
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.79
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.51
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.82
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.54
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.45
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.37
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.67
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4807.52
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.81
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.87
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.45
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.95
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9942
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.06
 p-value of test no 196                :  4.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.91
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.61
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.21
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9668.89
 p-value of test no 215                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.80
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.35
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.50
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.46
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12225.13
 p-value of test no 229                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.93
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.70
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999921176
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.11
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000006241
 
 Normal statistic for number of bits   :   0.049
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:12.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 M (L=50, r=25)      8.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98140181.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56356
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.49
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.96
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.10
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.10
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.19
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.54
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.51
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.62
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.19
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.85
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.40
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.30
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.13
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.44
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908781
   j =  2                              :            45605
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907751
   j =  2                              :            46117
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 92                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.73
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.12
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.01
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.44
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.11
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.89
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.70
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   17.23
 p-value of test no 134                :  6.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.73
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.88
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.79
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.46
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.19
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.93
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.50
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.44
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.96
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.48
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.14
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.46
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.57
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.63
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.95
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.72
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.62
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.39
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.27
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.13
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.44
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.52
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.73
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.53
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.64
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.68
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.14
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.72
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.52
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.05
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.33
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.87
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.41
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.48
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
 p-value of test no 212                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.57
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.21
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.56
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.45
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.19
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.66
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.94
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.92
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999999731
 
 Normal statistic for number of bits   : -2.13e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.36
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999986558
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.99
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:54.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         6.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99123221.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56357
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.08
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.14
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.49
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.28
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.38
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.04
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.82
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.44
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.34
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.97
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.52
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5199.50
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908710
   j =  2                              :            45639
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907846
   j =  2                              :            46065
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
 p-value of test no 100                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 102                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
 p-value of test no 112                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.02
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.73
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.39
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.03
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.35
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.94
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.19
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.49
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.57
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.99
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.34
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.80
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.96
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.82
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.10
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.79
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.83
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.75
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.90
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.20
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.23
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.84
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.12
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.51
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.83
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.37
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.82
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.27
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.61
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.81
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.94
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.81
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.51
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.31
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.50
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.32
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.93
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.08
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.02
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.85
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.41
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.67
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.05
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.22
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.06
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.37
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.10
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.40
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11537.18
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.16
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999966749
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.09
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999884993
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:24.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100007957.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56358
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.09
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    3.93
 p-value of test no 30                 :  9.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.38
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.83
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.63
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.36
 p-value of test no 51                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.13
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.42
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.99
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.55
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.62
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7242.81
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.78
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.79
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.68
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.88
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4840.96
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45452
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869452
   j =  1                              :        399909100
   j =  2                              :            45444
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908187
   j =  2                              :            45902
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-3
 p-value of test no 98                 :    0.9971
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.35
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.20
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.61
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.72
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.67
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.08
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.24
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.10
 p-value of test no 135                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.28
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17409.27
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.33
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.74
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.76
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.59
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.99
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.42
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.98
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.70
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.43
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.44
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.89
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.85
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.21
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.40
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.16
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.41
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.36
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.06
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.39
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.48
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.34
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.76
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.78
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.72
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.58
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.13
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.23
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.47
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.01
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.74
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10246.97
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-4
 p-value of test no 220                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 221                :  1.0e-2
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4609.55
 p-value of test no 222                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.64
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.36
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.79
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.04
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.59
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.97
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999962198
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.04
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999916226
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 242                :  5.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.54
 p-value of test no 243                :  5.6e-3
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:00.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101023765.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56359
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 15                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.32
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.34
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.01
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.57
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.82
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.07
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.64
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.66
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1574.02
 p-value of test no 56                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.64
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.14
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.86
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.14
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.79
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46049
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907906
   j =  2                              :            46041
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908189
   j =  2                              :            45898
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.78
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.06
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.19
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.94
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.37
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.25
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.70
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.77
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.66
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.44
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.29
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.76
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.38
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.38
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.82
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.89
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.16
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.53
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.31
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.40
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.93
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.56
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.34
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.13
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.40
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.86
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.48
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.24
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.33
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.52
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.39
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.00
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.25
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.34
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.97
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.69
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.63
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.19
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.15
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.16
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.65
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 206                :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.86
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.12
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.41
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
 p-value of test no 220                :    0.9963
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4681.30
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.01
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.10
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.30
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12171.30
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.68
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.59
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000024838
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.94
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000011950
 
 Normal statistic for number of bits   :   0.094
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:28.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102039574.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56360
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 16                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7101
 p-value of test no 18                 :    0.9945
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    3.74
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.53
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.11
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.41
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.10
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.24
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.13
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.52
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.40
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.54
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.91
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.41
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.85
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4928.60
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908147
   j =  2                              :            45925
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907744
   j =  2                              :            46122
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.30
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.47
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.85
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.52
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.22
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.73
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.68
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17854.10
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.71
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.85
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.47
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.14
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.21
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.33
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.36
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.23
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.64
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.50
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.41
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.07
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.28
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.13
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.28
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.78
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.32
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.74
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.97
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.26
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.96
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.85
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.75
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.17
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.43
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.33
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.45
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.10
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 181                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.94
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.88
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.37
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.52
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.34
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.42
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.22
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.66
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.10
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.13
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.84
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000146218
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.94
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999855650
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 246                :    0.9905
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:14.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82182152.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56361
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9921
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.85
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.93
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.40
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.89
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.22
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.26
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.75
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.19
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 59                 :    0.9918
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.63
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.08
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.73
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.94
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45552
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908900
   j =  2                              :            45544
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908926
   j =  2                              :            45534
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.73
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.52
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.56
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.12
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.38
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.50
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.71
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.91
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.77
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.23
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.71
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.78
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.82
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.39
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.83
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.71
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.43
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.34
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.75
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.45
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.20
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.84
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.37
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.63
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.00
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.36
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.67
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.35
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.86
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.53
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.59
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.19
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.08
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.90
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.88
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.19
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.04
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.21
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.49
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.48
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.65
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.08
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.72
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.90
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.13e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.59
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.69
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.76
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.90
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.56
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.45
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.69
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999877559
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.76
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999921572
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:04.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83329032.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56362
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.09
 p-value of test no 23                 :  8.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    3.36
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.75
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.61
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.43
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.46
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.27
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.69
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.51
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.40
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.38
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.22
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.82
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.86
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.79
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.56
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908705
   j =  2                              :            45646
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907888
   j =  2                              :            46050
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.26
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.19
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.08
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.85
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.36
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.94
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.97
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.09
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.95
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.78
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.44
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.13
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.45
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.41
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.96
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.17
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.52
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.43
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.79
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.88
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.73
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.12
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.82
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.35
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.91
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.17
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.73
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.13
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.13
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.49
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.13
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.46
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.85
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.09
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.09
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.64
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.97
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.24
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-3
 p-value of test no 194                :    0.99
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.37
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.55
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.12
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9753.94
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.43
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.65
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.55
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.32
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.92
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.34
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.50
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.56
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999942965
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.38
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999982808
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:37.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84017156.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56363
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4174
 p-value of test no 16                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.69
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.81
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.76
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.59
 p-value of test no 50                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.83
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.66
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.18
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.16
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.36
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1611.39
 p-value of test no 56                 :  8.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.22
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.68
 p-value of test no 59                 :  4.1e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.09
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.23
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.31
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.98
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908331
   j =  2                              :            45830
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45530
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869530
   j =  1                              :        399908943
   j =  2                              :            45524
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.99
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.68
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.37
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.18
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.58
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.00
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.20
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.95
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.48
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.96
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.71
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.67
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.29
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.71
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.48
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.23
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.59
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.77
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.78
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.18
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.74
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.20
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.90
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.42
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.47
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.22
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.35
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.19
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.86
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.93
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.42
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.63
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.39
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.28
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.77
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.18
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.93
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.88
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.48
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.85
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.84
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.15
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.48
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10180.49
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 220                :  5.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.25
 p-value of test no 221                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5136.46
 p-value of test no 222                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.92
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.32
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.66
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11430.96
 p-value of test no 229                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.43
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.49
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000052681
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.66
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000021676
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:28.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      8.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85819396.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56364
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.13
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.32
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.74
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.81
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.26
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.29
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.83
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.63
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.27
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.90
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.05
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.84
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.45
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.96
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908065
   j =  2                              :            45963
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908301
   j =  2                              :            45842
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.22
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.77
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.18
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.72
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.88
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.98
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
 p-value of test no 130                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.59
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.53
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.66
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.21
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17766.05
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.37
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.30
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.49
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.13
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.10
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.61
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.29
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.59
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.49
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.13
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.02
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.45
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.37
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.92
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.34
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.05
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.17
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.22
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.04
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.55
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.74
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.29
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.50
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.11
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.09
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.59
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.90
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.85
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.89
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.53
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.47
 p-value of test no 196                :    0.9932
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.02
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.35
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.81
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.23
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.9908
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.96
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.26
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.86
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12191.55
 p-value of test no 229                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.81
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.74
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000013144
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.58
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000066178
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:04.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86867972.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56365
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    4.59
 p-value of test no 38                 :  4.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.53
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.43
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.72
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.54
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.71
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.00
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.16
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.77
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.55
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.88
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.00
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.89
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.36
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.57
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908177
   j =  2                              :            45910
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908055
   j =  2                              :            45971
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.00
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.35
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.02
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.38
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.49
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.82
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.40
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.79
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.19
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.31
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.68
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.45
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.24
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.67
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.18
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.15
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.26
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.17
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.01
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.88
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.75
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.24
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.92
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.45
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.28
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.06
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.91
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.41
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.18
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.10
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.80
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.58
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.22
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5232.14
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.67
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.34
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.48
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.13
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.22
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.10
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.07
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.30
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.06
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.84
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.98
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.30
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.59
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.27
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.04
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000051820
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.18
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000023344
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:09.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87752708.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56366
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    3.96
 p-value of test no 38                 :  9.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.06
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.60
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.04
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.93
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  371.49
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.91
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6858.47
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.54
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.37
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.85
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.11
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.22
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908747
   j =  2                              :            45625
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908115
   j =  2                              :            45938
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.33
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.04
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.82
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.21
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.78
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-3
 p-value of test no 126                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.93
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.18
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.04
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17219.19
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.66
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.81
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.63
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.81
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.56
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.70
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.02
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.79
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.73
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.67
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.36
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.37
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.57
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.12
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.81
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.56
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.60
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.91
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.59
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.16
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.72
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.75
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.50
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.50
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.48
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.40
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.17
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.52
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.43
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.73
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.25
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.02
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.91
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.99
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.63
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.58
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.00
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.24
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.56
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.26
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000079957
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.96
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000102529
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:18.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88735748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56367
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1227
 p-value of test no 12                 : 1 -  8.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334347
   j =  1                              :        599997546
   j =  2                              :             1227
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.06
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.13
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.40
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.29
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.43
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.24
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.34
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.76
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.43
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.27
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.95
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.29
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908471
   j =  2                              :            45757
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907894
   j =  2                              :            46050
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.83
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.55
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.21
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.97
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.45
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.71
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.65
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.50
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.94
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.34
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.86
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.16
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.01
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.74
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.04
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.46
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.54
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.35
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.21
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.46
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.76
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.35
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.80
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.47
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.46
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.59
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.86
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.33
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.74
 p-value of test no 166                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.16
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.20
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.96
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.60
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.30
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.39
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.90
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.93
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.92
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.40
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 187                :    0.9987
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.33
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.93
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.95
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.67
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.19
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.78
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.07
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.77
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.34
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.61
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.69
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.84
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999929726
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.58
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000018451
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:27.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  8.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89784324.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56368
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.62
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.41
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.09
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.48
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.57
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.16
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.96
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.90
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.81
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.53
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.62
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.70
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.04
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908202
   j =  2                              :            45890
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908068
   j =  2                              :            45963
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-4
 p-value of test no 109                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-6
 p-value of test no 110                :    0.9983
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.52
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.63
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.99
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.31
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.13
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.67
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.29
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.50
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.28
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.93
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.19
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
 p-value of test no 138                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  170.76
 p-value of test no 141                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17218.06
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.93
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.88
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.84
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.94
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.68
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.36
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.03
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.50
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.90
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.15
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.41
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.29
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.86
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.92
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.34
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.21
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.53
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.29
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5299.89
 p-value of test no 168                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.19
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.73
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.48
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.62
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.67
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.25
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.26
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.04
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.45
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    3.91
 p-value of test no 184                :  5.4e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.82
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.78
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.55
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.98
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.82
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.26
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.52
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.69
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.73
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.59
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.42
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.96
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999886934
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.59
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999932276
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.15
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-3
 p-value of test no 251                :    0.9981
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:10.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90800132.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56369
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 5                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5535
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.54
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.52
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.76
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.55
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.16
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.11
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.98
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.41
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.98
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.60
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.54
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.68
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.35
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.80
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.71
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.76
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45231
 p-value of test no 70                 :    0.9988
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869231
   j =  1                              :        399909544
   j =  2                              :            45219
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908668
   j =  2                              :            45660
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 80                 :    0.9905
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 115                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.02
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.65
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.03
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.18
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.75
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.00
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.72
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.66
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.12
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17856.57
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.64
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.62
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.88
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.71
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.81
 p-value of test no 151                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.91
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.05
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.09
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.35
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.24
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.41
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.36
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.52
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.18
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.74
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.62
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.12
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.83
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.90
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.78
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.61
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.57
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.96
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.36
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4786.27
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.66
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.83
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.48
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.05
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 182                :  5.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.67
 p-value of test no 183                :    0.9962
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.83
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.92
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.65
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.60
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.29
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.24
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.59
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.19
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.74
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12148.99
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.92
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.94
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999933503
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.95
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999933392
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:30.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91783172.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56370
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 9                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    3.24
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.08
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.59
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.67
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.12
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.66
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.99
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.97
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1331.24
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.46
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.95
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.31
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.54
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.50
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.95
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908832
   j =  2                              :            45575
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908455
   j =  2                              :            45768
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.33
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.77
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.10
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.44
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.21
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.01
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.21
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.60
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.50
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.07
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.19
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.33
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.87
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.46
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.04
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.27
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.34
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.53
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.82
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.50
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.37
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.62
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.54
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.24
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.65
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.95
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.10
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.19
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.20
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.97
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.55
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.46
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.79
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.05
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.33
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.58
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.48
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.85
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.32
 p-value of test no 196                :    0.9953
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.59
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.72
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.53
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.63
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.78
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.74
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.75
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.42
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.16
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.33
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.77
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000137251
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.30
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000027220
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:29.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92831748.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56371
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7499
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.99
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.51
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.33
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.99
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.58
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.62
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.31
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.75
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.67
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.54
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.26
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.36
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.51
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.04
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.79
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908004
   j =  2                              :            45992
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908092
   j =  2                              :            45951
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.30
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.03
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.88
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.20
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.60
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.75
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.15
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.52
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.43
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.65
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.06
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.77
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.43
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.68
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.58
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.28
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.16
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.86
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.87
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.57
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.45
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.76
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.52
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.05
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.34
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.41
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.47
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.03
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.80
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.65
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.51
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.12
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.89
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.81
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.16
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  253.24
 p-value of test no 175                :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.72
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.11
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.15
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.31
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.25
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.25
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.77
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.77
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.94
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.33
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.68
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.37
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.18
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999973796
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.98
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999940994
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:38.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93749264.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56372
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 11                 :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    4.00
 p-value of test no 32                 :  8.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.02
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.69
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.27
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.22
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.98
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.36
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.29
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.93
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.58
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.19
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.82
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.10
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.90
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.84
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908263
   j =  2                              :            45864
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908598
   j =  2                              :            45698
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.71
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.17
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.29
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.86
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.75
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.86
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.19
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 127                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    6.39
 p-value of test no 128                :  6.9e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   71.03
 p-value of test no 129                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.70
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.55
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.06
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.18
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.58
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.41
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.13
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.13
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.05
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.60
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.86
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.23
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.90
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.95
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.73
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.36
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.86
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.88
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.08
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.57
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.37
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.13
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.60
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.86
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.55
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.09
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.73
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.80
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.73
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.24
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.08
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.35
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.85
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.13
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.80
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.29
 p-value of test no 217                :  4.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.10
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4708.58
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.62
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.33
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.37
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.64
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.85
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000170809
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.73
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000023821
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:38.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  93  HammingCorr, L = 300            4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94732304.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56373
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.05
 p-value of test no 47                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.24
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.76
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.40
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.85
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.59
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.54
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.52
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.96
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.28
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.88
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.94
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.86
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.51
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.89
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908087
   j =  2                              :            45949
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46351
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907301
   j =  2                              :            46345
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.90
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.90
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.45
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.97
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.32
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.43
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.76
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.33
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.11
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17437.38
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.15
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.39
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.10
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.42
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.25
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.56
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.78
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.66
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.95
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.68
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.83
 p-value of test no 157                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.77
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.05
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.57
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.67
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.31
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.63
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.08
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.21
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.56
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.03
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.48
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.08
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.47
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.89
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.58
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.51
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.56
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.85
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.84
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.11
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 182                :    0.9997    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.08
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-4
 p-value of test no 205                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.73
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.83
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.05
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.39
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.56
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.41
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.46
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.72
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.23
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.10
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999935531
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.46
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999891575
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:44.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95649808.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56374
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 9                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.19
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.43
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.48
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.26
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.78
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.41
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.29
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1553.07
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.69
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.45
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.75
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.77
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.35
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.57
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908489
   j =  2                              :            45751
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908117
   j =  2                              :            45934
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 97                 :    0.9900
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 98                 :  7.5e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 99                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.86
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.66
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.69
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.58
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.04
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.09
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.27
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.25
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.18
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.60
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.17
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.23
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.10
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.87
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.49
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.73
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.92
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.50
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.68
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.67
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.22
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.68
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.94
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.28
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.54
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.91
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.56
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.06
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.18
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.58
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.87
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.09
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.56
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.54
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.93
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.05
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.18
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.01
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.07
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 182                :  9.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 183                :    0.9931
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.67
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.99
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.55
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.80
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.53
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 224                :  1.3e-4    *****
 
 Anderson-Darling statistic = A2       :    7.46
 p-value of test no 225                :  2.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5246.70
 p-value of test no 226                :  2.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.25
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.07
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12193.88
 p-value of test no 229                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.57
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.31
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999957401
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.02
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000144391
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
 p-value of test no 240                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:43.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  96  HammingIndep, L=30, r=27        2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96534544.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56375
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.17
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.99
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.90
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.03
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.33
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.84
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.05
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.07
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.46
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6874.18
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.37
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.15
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.83
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.50
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.86
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908672
   j =  2                              :            45661
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908405
   j =  2                              :            45787
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.25
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.31
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.13
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.61
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.36
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.75
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.67
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.47
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.28
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.75
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.75
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.98
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.29
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.39
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.04
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.61
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.27
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.54
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.90
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.50
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.54
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.90
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.93
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.16
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.20
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.42
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.81
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.97
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.61
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.60
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.56
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.26
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.01
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.90
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.72
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.40
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.63
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.20
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.21
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.48
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.13
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.88
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.36
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.51
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.21
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.36
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.41
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.91
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.38
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.69
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999968531
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.85
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000193702
 
 Normal statistic for number of bits   :    1.53
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:13.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97550352.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56376
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 12                 :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.02
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.67
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.01
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.44
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.58
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.42
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.70
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.71
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.24
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.58
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.87
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.34
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907787
   j =  2                              :            46096
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908386
   j =  2                              :            45804
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.31
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.46
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.80
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.11
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.87
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.79
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.24
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17162.87
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.27
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.68
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.93
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.07
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.54
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.83
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.78
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.25
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.95
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.66
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.39
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.60
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.17
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.33
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.64
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.45
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.82
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.40
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  468.32
 p-value of test no 166                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.41
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.99
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.12
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.71
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.79
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.61
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.09
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.32
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.74
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.48
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.16
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.42
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 210                :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9620.32
 p-value of test no 211                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.47
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.58
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.38
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.91
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.39
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.71
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.27
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.62
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000101815
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.41
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000069616
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    2.33
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:56.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98566160.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56377
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.02
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.23
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.34
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.35
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.19
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.32
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.61
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.48
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.81
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.68
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.37
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.93
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.84
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.41
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46278
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870278
   j =  1                              :        399907445
   j =  2                              :            46276
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907928
   j =  2                              :            46033
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 91                 :    0.9941
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.20
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.97
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.54
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.82
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.11
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.22
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.74
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
 p-value of test no 143                :    0.9962
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17080.74
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.68
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.33
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.30
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.48
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.52
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.29
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.05
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.18
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.80
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.66
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.78
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.03
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.51
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.73
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.46
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.80
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.74
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.55
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.45
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.28
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.59
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.86
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.15
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.38
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.73
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.84
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.14
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.61
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.14
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.91
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.11
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.16
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.78
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.83
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.45
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.35
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.55
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.26
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999992156
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.60
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999928646
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.093
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:22.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99549200.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56378
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5540
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 38                 :    0.9988
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.74
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.24
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.28
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.68
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.51
 p-value of test no 51                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.91
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.39
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.17
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1542.35
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.73
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.99
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.84
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.19
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.25
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.76
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908747
   j =  2                              :            45616
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908026
   j =  2                              :            45987
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.94
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.17
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.43
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.71
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.61
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.87
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.33
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.25
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.09
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.88
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.78
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.08
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.93
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.39
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.32
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.70
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.29
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.10
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.67
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.84
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.75
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.44
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.54
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.32
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.30
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.03
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.73
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.43
 p-value of test no 167                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.99
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.10
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.69
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.37
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  472.12
 p-value of test no 172                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.65
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.10
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.43
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.95
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.72
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.27
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.74
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.38
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.61
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.77
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.83
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.24
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.12
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.36
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.92
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.78
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000131422
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.60
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999901406
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 251                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:29.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100565008.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56379
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    3.36
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.21
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.00
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.75
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.29
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  501.38
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.78
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.97
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.47
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.81
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.14
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.63
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907656
   j =  2                              :            46172
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908092
   j =  2                              :            45948
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.27
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.05
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.37
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.44
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.56
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.51
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.41
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.01
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.39
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.37
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.84
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
 p-value of test no 143                :    0.9971
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17069.00
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.55
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.19
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.26
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.43
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.39
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.09
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.67
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.80
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.01
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.21
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.33
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.78
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.05
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.88
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.31
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.59
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.81
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.14
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.27
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.62
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.73
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.73
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.66
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.76
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.02
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.55
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.36
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.10
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.79
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.96
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.49
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.70
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.23
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.77
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.23
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.77
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.46
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.89
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.70
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.27
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.49
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.06
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000147232
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.40
 p-value of test no 233                :    0.9913
 
 
 -----------------------------------------------
 Total number of bits:  8000050776
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:58.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101580816.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56380
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.39
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.83
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.31
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.75
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.18
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.57
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.41
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.89
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.79
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.44
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.19
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
 p-value of test no 59                 :    0.9967
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.00
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.87
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.33
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.61
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.95
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908268
   j =  2                              :            45857
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908394
   j =  2                              :            45797
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.90
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.24
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.30
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.17
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.05
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.17
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.97
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.70
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.68
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.03
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17830.46
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.77
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.70
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.87
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.70
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.92
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.98
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.73
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.15
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.93
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.93
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.33
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.21
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.27
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.51
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.00
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.17
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.58
 p-value of test no 162                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.44
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.47
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.28
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.25
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.72
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.42
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.00
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.54
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.63
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.52
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.39
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.38
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.34
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.77
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9944
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.43
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.85
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.30
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.56
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.09
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.38
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.27
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.20
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11536.97
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11602.67
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.81
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000017827
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.59
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999972275
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:16.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82214921.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56381
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997357
   j =  2                              :             1320
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.07
 p-value of test no 35                 :  2.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.69
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.56
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.10
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.07
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.48
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.45
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7244.67
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.60
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.41
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.95
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.31
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46266
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870266
   j =  1                              :        399907471
   j =  2                              :            46260
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45363
 p-value of test no 71                 :    0.9921
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869363
   j =  1                              :        399909277
   j =  2                              :            45357
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.96
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.89
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.90
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.09
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.91
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.09
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.88
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.42
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.82
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.025
 p-value of test no 135                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.00
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17079.16
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.99
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.73
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.67
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.37
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   70.09
 p-value of test no 152                :  3.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.60
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.93
 p-value of test no 156                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.00
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.97
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.25
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.81
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.47
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.11
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.26
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.38
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.83
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.94
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.46
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.35
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.63
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.69
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.08
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.55
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.64
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.12
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.46
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.31
 p-value of test no 176                :    0.9987
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.16
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.12
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.67
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.68
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.84
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.58
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.69
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.67
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.87
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.57
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4303.89
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.12
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.60
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.67
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000024121
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.82
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000069151
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    2.13
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:21.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 M (L=50, r=25)      3.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83394566.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56382
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4200
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.80
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.60
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.35
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.00
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.26
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.07
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.22
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.37
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.76
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.60
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.21
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.45
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.09
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908533
   j =  2                              :            45726
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908249
   j =  2                              :            45868
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.26
 p-value of test no 116                :  5.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.07
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.77
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.25
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.61
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.21
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.71
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.85
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.50
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17185.02
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.11
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.08
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.95
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.62
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.91
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.61
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.16
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.95
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.11
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.11
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.67
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.82
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.84
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.58
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.77
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.10
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.92
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.09
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.51
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.14
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.29
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.42
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.62
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.73
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.93
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.30
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.34
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.35
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.00
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 185                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 186                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    6.94
 p-value of test no 187                :  3.9e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.66
 p-value of test no 188                :  1.3e-4    *****
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.08
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.79
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.11
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10340.70
 p-value of test no 211                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.20
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.58
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.60
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.70
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.89
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.15
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.55
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.33
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000103453
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.99
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999925817
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:39.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               5.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  83  LempelZiv, r = 15               1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84344838.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56383
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 17                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.02
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.68
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.90
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.66
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.12
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.42
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.09
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.74
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.06
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.39
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.93
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.26
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.12
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.01
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907917
   j =  2                              :            46034
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908504
   j =  2                              :            45739
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 103                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.30
 p-value of test no 119                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.98
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.21
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.26
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.70
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.71
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.22
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.95
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.08
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17699.45
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.15
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.16
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.38
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.16
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.80
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.19
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.97
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.49
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.09
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.31
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  187.26
 p-value of test no 159                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.12
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.86
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.79
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.61
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.56
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.27
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.66
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.32
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.42
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.52
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.25
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.95
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.27
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.03
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 201                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.92
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.67
 p-value of test no 204                :  2.8e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    6.60
 p-value of test no 206                :  5.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  139.13
 p-value of test no 207                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.11
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.68
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.40
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.91
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.88
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.84
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.49
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.11
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.73
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000085786
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.98
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999925592
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:58.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  89  PeriodsInStrings, r = 20        0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85360646.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56384
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 6                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 12                 :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.29
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.90
 p-value of test no 49                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.97
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.19
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.52
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.97
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.95
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.35
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.77
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.42
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.06
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.64
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.69
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.62
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907874
   j =  2                              :            46060
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908521
   j =  2                              :            45732
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 99                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 108                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.99
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.97
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.98
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.54
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.16
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.33
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.59
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.70
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.59
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.01
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.91
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.02
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.29
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.98
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.79
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.44
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.58
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.46
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.48
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.63
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.98
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.64
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.02
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.69
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.66
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.49
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.79
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.33
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.02
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.12
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.02
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.54
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.16
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.03
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.90
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.21
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.66
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.93
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.66
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.43
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.65
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.67
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 209                :  2.7e-3
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10261.96
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.83
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.08
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.46
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.31
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.77
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11473.91
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11607.59
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.80
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999901865
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.85
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000026341
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:11.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           7.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86245382.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56385
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.64
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.57
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.17
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.47
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.84
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.71
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.13
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.94
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.18
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.10
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.82
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.34
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.15
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.87
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.89
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908470
   j =  2                              :            45762
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908151
   j =  2                              :            45920
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 115                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.72
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.33
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.61
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.19
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.17
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.36
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.01
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17324.05
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   14.78
 p-value of test no 146                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.43
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.10
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.83
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.80
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.32
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.63
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.57
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.14
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.01
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.92
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.53
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.91
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.59
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.16
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.71
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.71
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.92
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.41
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.46
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.46
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.03
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.54
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.50
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  253.91
 p-value of test no 170                :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.70
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.33
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.49
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.45
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.77
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.96
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.91
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.75
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.18
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.76
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.79
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 218                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.26
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.28
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.37
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.72
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12085.28
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.16
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.72
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000080851
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.67
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000123568
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:15.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87261190.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56386
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.47
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.87
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.39
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.22
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.76
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.17
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.90
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.32
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1546.16
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.70
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.24
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.68
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.21
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.16
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.17
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908498
   j =  2                              :            45742
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907669
   j =  2                              :            46158
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.78
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.14
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.95
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.50
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.36
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.39
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.67
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.82
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.59
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.64
 p-value of test no 137                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.12
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17416.16
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.72
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.09
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.08
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.80
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.17
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.01
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.19
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.22
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.92
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.57
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.82
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.08
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.40
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.94
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.58
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.07
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.42
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.60
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.89
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.04
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.30
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.68
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.65
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.49
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.98
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.59
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.60
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.34
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.82
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.27
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.09
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.66
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.54
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.38
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.24
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.49
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12234.78
 p-value of test no 230                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.81
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000125716
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.58
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999947774
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:15.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88178694.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56387
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 24                 :    0.9989
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    3.75
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.12
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.94
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.84
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.56
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.47
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.92
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.41
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.35
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.70
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.51
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7106.12
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 58                 :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.23
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.56
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.49
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.14
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908457
   j =  2                              :            45767
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908461
   j =  2                              :            45762
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.03
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.33
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.31
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.62
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.10
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.79
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.19
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.42
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.08
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.91
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.98
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.32
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.35
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.49
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.43
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.17
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.16
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.47
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.15
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.30
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.69
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.98
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.89
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.17
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.76
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.07
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.12
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.89
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.19
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.39
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.93
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.51
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.64
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.82
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.09
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.74
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.79
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.60
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.34
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.17
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.44
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.14
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
 p-value of test no 220                :    0.9964
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4723.83
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.09
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.44
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.19
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.97
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.95
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000099847
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.24
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999898718
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:52.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89292806.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56388
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9951
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   40.72
 p-value of test no 48                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.74
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.69
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.55
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.18
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.02
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.73
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.04
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.56
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.76
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.88
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.90
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908423
   j =  2                              :            45787
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.66
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.25
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.19
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.96
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.61
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.67
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.80
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.28
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.55
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.18
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.32
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.41
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.33
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.45
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.17
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.76
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.05
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.48
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.07
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.81
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.38
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.94
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.37
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.39
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.23
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.85
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.12
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.28
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.00
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.25
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.81
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.58
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.22
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.54
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.30
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.12
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.69
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.85
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.00
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.03
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.12
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.55
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.19
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.59
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.89
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.32
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.42
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.75
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.28
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.95
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.78
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999930644
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.50
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999977621
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:31.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90275846.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56389
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    3.82
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.18
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.27
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.44
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.53
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.35
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.08
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1552.04
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.95
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.80
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.10
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.69
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.96
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.79
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907562
   j =  2                              :            46216
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908434
   j =  2                              :            45777
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  7.8e-3
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
 p-value of test no 110                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.21e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.62
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.02
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.99
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.18
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.01
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.68
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.18
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.72
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.47
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.57
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.73
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.06
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.84
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.58
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.97
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.23
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.25
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.31
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.55
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.50
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.98
 p-value of test no 159                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.42
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.08
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.41
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.35
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.13
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.41
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.99
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.53
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.27
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.45
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.20
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.85
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.51
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.96
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.09
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.57
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.14
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.47
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.17
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.12
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.54
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.16
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.82
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.23
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.50
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.18
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.12
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.23
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.17
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999987830
 
 Normal statistic for number of bits   :  -0.096
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.58
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000001285
 
 Normal statistic for number of bits   :   0.010
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:52.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91357190.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56390
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5574
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.30
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    4.01
 p-value of test no 38                 :  8.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.63
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.38
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.22
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.16
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.77
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.22
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.93
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7279.99
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.48
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.88
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.23
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4938.14
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908035
   j =  2                              :            45978
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908389
   j =  2                              :            45795
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.74
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.47
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.37
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.80
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.22
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.05
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.77
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.17
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.59
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.11
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.41
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.43
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.56
 p-value of test no 151                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.73
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.69
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.95
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.44
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.61
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.72
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.04
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.81
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.72
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.28
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.23
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.31
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.45
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.23
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.46
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.05
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.16
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.30
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.94
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.60
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.35
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.63
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.63
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.44
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.87
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.41
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.01
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.18
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.69
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.52
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.90
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.89
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.60
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.54
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.59
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000005467
 
 Normal statistic for number of bits   :   0.043
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.26
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000097744
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.63
 p-value of test no 238                :    0.9957
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    2.17
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:18.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92340230.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56391
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9914
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.61
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.16
 p-value of test no 47                 : 1 -  1.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.54
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.07
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.89
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.30
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.91
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.14
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.72
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.31
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.36
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.57
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.97
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.53
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.20
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46190
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870190
   j =  1                              :        399907625
   j =  2                              :            46180
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908673
   j =  2                              :            45662
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.75
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.37
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.50
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.66
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.04
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.92
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.87
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.93
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.37
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.06
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.06
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.05
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.26
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.77
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.74
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.98
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.54
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.50
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.44
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.49
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.20
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.77
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.98
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.44
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.60
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.64
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.61
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.55
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.85
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.68
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.24
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.03
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.73
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.52
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.89
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.19
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.82
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 180                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.08
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.05
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.49
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.15
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.62
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.60
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.20
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.43
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.98
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.07
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.56
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.13
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999995936
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.71
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000138880
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:04.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27              1 -  1.2e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93388806.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56392
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.49
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.53
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.84
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.26
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.77
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.20
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.40
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.21
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.37
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.17
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.87
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.68
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.50
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.59
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908695
   j =  2                              :            45645
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908431
   j =  2                              :            45777
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 93                 :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 94                 :  2.9e-4    *****
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 95                 :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  4.8e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.63
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.25
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.27
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.29
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.02
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.16
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.55
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.03
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.64
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.13
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.09
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.71
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.60
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.06
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.09
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.99
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.71
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.65
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.05
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.44
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.70
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.53
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.97
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.99
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.18
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.61
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.73
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.04
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.05
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.55
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.52
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.54
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.03
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.22
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.10
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.01
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.49
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.50
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.82
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.02
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.39
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.03
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.18
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.94
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.73
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.43
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.70
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.86
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000072055
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.49
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000011014
 
 Normal statistic for number of bits   :   0.087
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:53.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  4.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94470150.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56393
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.02
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.84
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.91
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.28
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.79
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.28
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.44
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1305.39
 p-value of test no 56                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6796.72
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.29
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.45
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.49
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.36
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.33
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908102
   j =  2                              :            45949
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908431
   j =  2                              :            45777
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.72
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.89
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.96
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.18
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.64
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.75
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.79
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.51
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.80
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.59
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.58
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.94
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.78
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.21
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.06
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.53
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.44
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.80
 p-value of test no 154                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.99
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.40
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.73
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.99
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.08
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.41
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.33
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.19
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.35
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.15
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.66
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.84
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.48
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.14
 p-value of test no 169                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.31
 p-value of test no 170                :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.11
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.63
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.75
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.29
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.24
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 180                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.17
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.99
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.42
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.24
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.38
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.65
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.75
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.12
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.02
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.70
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.01
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.20
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000086596
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.23
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000074914
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:07.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95485958.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56394
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9942
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.09
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.56
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.53
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.26
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.47
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.67
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.19
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.88
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.35
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.04
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.49
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.04
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.03
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908228
   j =  2                              :            45883
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45326
 p-value of test no 71                 :    0.9951
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869326
   j =  1                              :        399909350
   j =  2                              :            45322
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.67
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.56
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.05
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.77
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.23
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.13
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.77
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.96
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-4
 p-value of test no 142                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17915.61
 p-value of test no 145                :  4.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.73
 p-value of test no 146                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.70
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.31
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.62
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.46
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.41
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.95
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.73
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.33
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.39
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.16
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.15
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.26
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.48
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.39
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.69
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.69
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.55
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.09
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.51
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.95
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.41
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.19
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.67
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.35
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.12
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.02
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.33
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.48
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.28
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10242.08
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.38
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.95
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.15
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.95
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.47
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.66
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.04
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.72
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000195019
 
 Normal statistic for number of bits   :    1.54
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.91
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000006265
 
 Normal statistic for number of bits   :   0.050
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:56.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96468998.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56395
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4201
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    3.24
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.51
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.42
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.26
 p-value of test no 50                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.22
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.84
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.66
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.59
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.05
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.60
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.58
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.43
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.67
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.18
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908087
   j =  2                              :            45952
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908309
   j =  2                              :            45841
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 103                :    0.9900
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.31
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.62
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.76
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.53
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.16
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.81
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.25
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.12
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.25
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.69
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.01
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.90
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.80
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.98
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.20
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.30
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.15
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.32
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  583.01
 p-value of test no 158                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.44
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.20
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.81
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.38
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.19
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.44
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.36
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.31
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.02
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.02
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.62
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.29
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.07
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.50
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.90
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.47
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.23
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.28
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.27
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.35
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.16
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9758.59
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.81
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.39
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 223                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
 p-value of test no 224                :    0.9978
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4646.88
 p-value of test no 226                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.55
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.06
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.82
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.95
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.99
 p-value of test no 231                :  3.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999919154
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.33
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000042025
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:30.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97484806.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56396
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4174
 p-value of test no 16                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.02
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.89
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.03
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.39
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.77
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.96
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.96
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.69
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.50
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.76
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.43
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.79
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.73
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.66
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908078
   j =  2                              :            45952
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908229
   j =  2                              :            45878
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.68
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.40
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.56
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.24
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.21
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.92
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.04
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.31
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.56
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.81
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.72
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.37
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.71
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.64
 p-value of test no 153                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.12
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.53
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.83
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.00
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.40
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.21
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.93
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.99
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.76
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.24
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.56
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.64
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.13
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.53
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.57
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.48
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.16
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.84
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.51
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.90
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.18
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.78
 p-value of test no 178                :  1.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.10
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 204                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.63
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 208                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10386.59
 p-value of test no 211                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.06
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.86
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 223                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    4.68
 p-value of test no 225                :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4627.29
 p-value of test no 226                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.68
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.64
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.42
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12161.87
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.79
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000034237
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.87
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999955532
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:59.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99057670.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56397
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.02
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.05
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.95
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.00
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.00
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.75
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.53
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.69
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.43
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
 p-value of test no 59                 :    0.9904
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.49
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.80
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.00
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.88
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5250.24
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908677
   j =  2                              :            45660
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908547
   j =  2                              :            45725
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.82
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.16
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.47
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.36
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.96
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.57
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.23
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.03
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.21
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.10
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 142                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 143                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 144                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17957.02
 p-value of test no 145                :  2.6e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.46
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.56
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.83
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.12
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.57
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.30
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.65
 p-value of test no 153                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.10
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.18
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.69
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.93
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.89
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.91
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.56
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   99.42
 p-value of test no 161                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.13
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.60
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.30
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.04
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.67
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.16
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.51
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.64
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.13
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.85
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.50
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.85
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.34
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.29
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.78
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.16
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 200                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-3
 p-value of test no 201                :    0.9976
 
 Anderson-Darling statistic = A2       :    5.10
 p-value of test no 202                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  141.35
 p-value of test no 203                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.14
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.59
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.12
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.82
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.37
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.11
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.59
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.09
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.35
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.74
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999978803
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.66
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000048403
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:15.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  88  PeriodsInStrings, r = 0         0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100073478.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56398
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997321
   j =  2                              :             1338
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.60
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    4.20
 p-value of test no 39                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.33
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.76
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.52
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.93
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.66
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.95
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.04
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.22
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.04
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.33
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.28
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907681
   j =  2                              :            46152
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907825
   j =  2                              :            46083
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.60
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.97
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.89
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.50
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.46
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.63
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.53
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.78
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.50
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.37
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.21
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17158.32
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.95
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.59
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.24
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.46
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.98
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.61
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.33
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.68
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.64
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.77
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.61
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.90
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.43
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.75
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.85
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.24
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.35
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.13
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.15
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.83
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.73
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.93
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.91
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.73
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.83
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.40
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.79
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.00
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.35
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.30
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.25
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.73
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.92
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.40
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.13
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.53
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.60
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.42
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.26
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999952076
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.23
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000006349
 
 Normal statistic for number of bits   :   0.050
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:20.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101056518.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56399
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 8                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.31
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.78
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.73
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.13
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.26
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.57
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.34
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.56
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.43
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.76
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 62                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.69
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.39
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.52
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908331
   j =  2                              :            45827
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46329
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870329
   j =  1                              :        399907349
   j =  2                              :            46315
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.64
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.99
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.10
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.61
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.89
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.15
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.15
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.38
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.15
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.36
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.03
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.62
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.38
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.81
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.40
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.65
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.28
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.17
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.39
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.78
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.72
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.97
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.84
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.18
 p-value of test no 162                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.88
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.54
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.86
 p-value of test no 165                :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.65
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.32
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.45
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.22
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.32
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.46
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.44
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.82
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.38
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.71
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.07
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   25.91
 p-value of test no 196                :  1.1e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.55
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.34
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.64
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.92
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.32
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.04
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.06
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.73
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.77
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.18
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.91
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999859973
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.97
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000079027
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:08.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102105094.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56400
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997425
   j =  2                              :             1286
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7111
 p-value of test no 21                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    3.06
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.34
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.75
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.59
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.05
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.33
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.44
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.86
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.43
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.97
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1585.54
 p-value of test no 56                 :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.43
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.18
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.38
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.53
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4944.64
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908624
   j =  2                              :            45688
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907972
   j =  2                              :            46008
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 74                 :  5.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9969
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 81                 :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9972
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.63
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.75
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.68
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.30
 p-value of test no 123                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.20
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.61
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.59
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.17
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.09
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.44
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.50
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.45
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.58
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.14
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.30
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.13
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.41
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.14
 p-value of test no 156                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.48
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.42
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.93
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.22
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.88
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.98
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.94
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.63
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.40
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.89
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.17
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.83
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.11
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.77
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.81
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.95
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.82
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.97
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.16
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.40
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.81
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.94
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.92
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.28
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.68
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.40
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.53
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.87
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.10
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12289.63
 p-value of test no 229                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.28
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.66
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999852671
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.06
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999905315
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    2.33
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 253                :    0.11
 
 Sample variance                       :    2.02
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:27.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82247690.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56401
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5261
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.40
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.57
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.13
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.22
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.71
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.95
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.33
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.76
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.76
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.81
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.53
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.56
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908787
   j =  2                              :            45605
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46212
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870212
   j =  1                              :        399907583
   j =  2                              :            46198
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
 p-value of test no 94                 :    0.9954
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.15
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.57
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.69
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.66
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.10
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.13
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.84
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.58
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17794.49
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.88
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.87
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.28
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.56
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.64
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.35
 p-value of test no 153                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.44
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.46
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.74
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.24
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.83
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.89
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.31
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.77
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.46
 p-value of test no 162                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.26
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.43
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.10
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.22
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.07
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.40
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.62
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.57
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.01
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.19
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5239.13
 p-value of test no 173                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.37
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.22
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.26
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.67
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-3
 p-value of test no 194                :    0.99
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.67
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.82
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.71
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.60
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.40
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.22
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.06
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.85
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.83
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.17
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.89
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000006640
 
 Normal statistic for number of bits   :   0.052
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.86
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999965462
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:07.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82935818.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56402
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.85
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.62
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.87
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.58
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.58
 p-value of test no 52                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   91.54
 p-value of test no 53                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.46
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.86
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.49
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6773.88
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.16
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.27
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.55
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.17
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.71
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45491
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869491
   j =  1                              :        399909023
   j =  2                              :            45481
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908686
   j =  2                              :            45657
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.27
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.68
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.01
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.26
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.82
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.09
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.63
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.72
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.29
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.91
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.89
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.41
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.79
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.49
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.89
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.57
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.99
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.99
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.98
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.36
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.98
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.20
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.44
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.08
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.65
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.49
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.02
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.91
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.09
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.86
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.15
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.03
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.96
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.02
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.44
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.79
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.90
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-4
 p-value of test no 194                :    0.9950
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.43
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.04
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.90
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.63
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.42
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.34
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.82
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.81
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.19
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.46
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.66
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.31
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000118558
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.77
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000002623
 
 Normal statistic for number of bits   :   0.021
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.22
 p-value of test no 249                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:52.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84082698.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56403
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.26
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.71
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.47
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.73
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.45
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6826.60
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.47
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.91
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.21
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4884.55
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908347
   j =  2                              :            45825
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908147
   j =  2                              :            45922
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.52
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.49
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.33
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.26
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.03
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.77
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.80
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.73
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.87
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.21
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.07
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17409.93
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.42
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.48
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.58
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.21
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.51
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.99
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.55
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.55
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.47
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.40
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.57
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.27
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.81
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.73
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.16
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.24
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.18
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.88
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.47
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4827.42
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.04
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.16
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.41
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.69
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.78
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.41
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.43
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.09
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.09
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.79
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.73
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10304.55
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.77
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.26
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.31
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.24
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12112.11
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.49
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.74
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999963812
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.58
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000003127
 
 Normal statistic for number of bits   :   0.025
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:56.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85426186.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56404
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 11                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    4.53
 p-value of test no 44                 :  4.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.70
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.19
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.57
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.98
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.83
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.18
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.55
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.33
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.64
 p-value of test no 61                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.71
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.24
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.31
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.03
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908227
   j =  2                              :            45879
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908578
   j =  2                              :            45705
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.90
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.34
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.90
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.76
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.16
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.73
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.29
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.88
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.24
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.77
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.51
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.27
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.11
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.46
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.54
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.41
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.28
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.72
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.03
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.02
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.30
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.76
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.10
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.79
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.53
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.81
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.30
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.47
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.36
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.89
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.58
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.46
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.16
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.46
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.03
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.64
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.49
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.36
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.91
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.72
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.53
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.67
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.83
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.10
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.63
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4357.21
 p-value of test no 227                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.10
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.47
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.23
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.05
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999951116
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.96
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000035947
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.95
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:46.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86441994.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56405
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9955
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    3.82
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.01
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.16
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.43
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.11
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.13
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.46
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.02
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.34
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.00
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.32
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908148
   j =  2                              :            45920
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908525
   j =  2                              :            45733
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.46
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.83
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.27
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.70
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.79
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.32
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.44
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.92
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.02
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.83
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.51
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.43
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.13
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.17
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.39
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.07
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.21
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.57
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.94
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.84
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.92
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.33
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.77
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.46
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.25
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.33
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.75
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.29
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.59
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.05
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.13
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.68
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.87
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.40
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.17
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.60
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   33.09
 p-value of test no 178                :  9.4e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.97
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 186                :  1.0e-3
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.23
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.94
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.98
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.91
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.47
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.94
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.32
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.72
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.40
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.03
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.90
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.81
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.49
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999987302
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.15
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000076408
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 245                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:29.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  81  LinearComp, r = 0               9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87490570.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56406
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.14
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.96
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.34
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.73
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.69
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.07
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.80
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.23
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.66
 p-value of test no 58                 :  5.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.43
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.56
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.52
 p-value of test no 66                 :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.03
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.27
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908428
   j =  2                              :            45777
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45548
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908907
   j =  2                              :            45542
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.94
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.44
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.76
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.46
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   70.35
 p-value of test no 129                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.20
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.07
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.07
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.73
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.14
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.78
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.33
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.50
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.85
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.75
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.15
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.89
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.80
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.69
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.49
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.10
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.38
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.02
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.13
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.96
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.95
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.64
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.51
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.27
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.72
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.96
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.51
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.07
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.16
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.99
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.44
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.27
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.81
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.80
 p-value of test no 196                :    0.9992    *****
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.44
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.35
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.06
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.12
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.40
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.05
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.82
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.50
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.96
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.15
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.31
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000007111
 
 Normal statistic for number of bits   :   0.056
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   88.88
 p-value of test no 233                :  2.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000136378
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.028
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:14.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  86  LongestHeadRun, r = 0           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88309770.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56407
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7612
 p-value of test no 19                 :  3.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.08
 p-value of test no 29                 :  9.4e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.96
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.62
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.95
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.02
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.33
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.39
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.75
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.23
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.27
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.40
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.59
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.95
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.05
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908118
   j =  2                              :            45938
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908217
   j =  2                              :            45890
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.58
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.52
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.38
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.83
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.72
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.39
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.88
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.44
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.55
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.94
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17659.28
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.43
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.67
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.95
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.69
 p-value of test no 149                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.89
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.61
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.38
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.89
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.65
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.56
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.49
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.69
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  431.61
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.62
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.63
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.27
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.41
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.47
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.34
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.40
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.72
 p-value of test no 166                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.44
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.69
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.01
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.73
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.85
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.51
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.28
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.61
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.96
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.38
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.12
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.06
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.28
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.89
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10190.35
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.25
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.42
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.92
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.20
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.97
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.69
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.57
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000011854
 
 Normal statistic for number of bits   :   0.094
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.70
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999953546
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:38.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  19  BirthdaySpacings, t = 8         3.3e-4
  23  ClosePairs mNP, t = 5           9.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89358346.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56408
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 3                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    4.51
 p-value of test no 26                 :  4.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.33
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.53
 p-value of test no 34                 :  5.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.11
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.19
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.25
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.50
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.23
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.02
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.06
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.36
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.95
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.71
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.69
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.38
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.74
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908448
   j =  2                              :            45776
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908270
   j =  2                              :            45856
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 94                 :    0.9937
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    4.56
 p-value of test no 102                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.47
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.18
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.18
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.94
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.88
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.27
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.96
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.41
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17496.03
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.91
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.86
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.91
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.43
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.28
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.16
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.97
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.75
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.21
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.00
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.50
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.72
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.41
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.67
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.09
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.73
 p-value of test no 166                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.66
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.86
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.34
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.89
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.36
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.84
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.54
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.06
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.55
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.80
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.96
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.48
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.19
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.65
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.01
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.12
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.00
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.29
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.93
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.68
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.31
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.65
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.33
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000019951
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.32
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000100963
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.93
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90439690.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56409
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     986
 p-value of test no 25                 :  2.5e-3
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.19
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.30
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.93
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.54
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.26
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.61
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.57
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.69
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.80
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.82
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.77
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.42
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.48
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.56
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4919.28
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907578
   j =  2                              :            46205
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908102
   j =  2                              :            45946
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.38
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.20
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.71
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.08
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.75
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.18
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.63
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.60
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.19
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.18
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.63
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.18
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.54
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.24
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.06
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.25
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.04
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.70
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.62
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.57
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.84
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.29
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.43
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.48
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.96
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.42
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.26
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.98
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.81
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.67
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.77
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.65
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.53
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.04
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.70
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.09
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.85
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.10
 p-value of test no 184                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.71
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.91
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.60
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.76
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.58
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.69
 p-value of test no 218                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.20
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.36
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.76
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.07
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.38
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.99
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.49
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999967364
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.95
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000073417
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.073
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:45.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91521034.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56410
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5315
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.49
 p-value of test no 35                 :  5.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.33
 p-value of test no 40                 :  7.8e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.26
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.64
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.16
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.25
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.32
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.58
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.70
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.69
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.30
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6843.70
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.85
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.16
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.02
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.94
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.78
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907980
   j =  2                              :            46007
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908723
   j =  2                              :            45631
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
 p-value of test no 80                 :    0.9936
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-5
 p-value of test no 113                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.36
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.29
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.24
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.83
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.89
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.68
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.26
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.31
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.89
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17503.80
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.99
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.92
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.78
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.72
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.76
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.48
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.49
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.79
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.89
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.91
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.08
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.32
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.23
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.35
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.79
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.09
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.87
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.16
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.75
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.52
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.44
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.56
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.96
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.94
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  493.81
 p-value of test no 174                :  5.5e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.22
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.65
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.68
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 204                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 206                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.18
 p-value of test no 207                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.95
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.78
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.50
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.73
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.97
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.78
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.27
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.71
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.57
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999988373
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.18
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000179524
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:36.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NP, t = 16           7.8e-4
  79  RandomWalk1 R (L=10000, r=15)   5.5e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92569610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56411
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 10                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.01
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.56
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.02
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.46
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.29
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.41
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.79
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.25
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.91
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.07
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.50
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.01
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.77
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.22
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907862
   j =  2                              :            46069
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45698
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869698
   j =  1                              :        399908607
   j =  2                              :            45692
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.83
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.92
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.92
 p-value of test no 121                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.64
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.20
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.36
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.52
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.56
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.18
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.56
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17577.53
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.82
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.02
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.67
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.15
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.21
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.70
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.08
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.95
 p-value of test no 154                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.57
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.52
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.56
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.22
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.33
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.21
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.35
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.73
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.62
 p-value of test no 164                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.63
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.35
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.09
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.08
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.68
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.03
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.16
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.60
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.88
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.95
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.60
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.83
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.89
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.13
 p-value of test no 198                :    0.9973
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.78
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.88
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.91
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.03
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4719.60
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.16
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.31
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.40
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.76
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.94
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.02
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999888266
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.32
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999866411
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:39.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93454349.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56412
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 10                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7103
 p-value of test no 15                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.42
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.57
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.35
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.53
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.40
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.11
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.62
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.84
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.76
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.98
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.02
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.28
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.54
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.67
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45578
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869578
   j =  1                              :        399908848
   j =  2                              :            45570
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46093
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907820
   j =  2                              :            46081
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    5.13
 p-value of test no 95                 :  2.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9989
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.55
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.64
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.35
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.41
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.54
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.03
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.26
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.53
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.75
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17550.46
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.00
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.61
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.34
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.54
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.51
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.78
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.53
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.72
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.84
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.21
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.98
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.97
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.51
 p-value of test no 162                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.48
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.31
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.54
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.39
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.21
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.79
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.08
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.80
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.74
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.78
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.42
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.64
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.98
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.87
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.60
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.89
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.25
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.04
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.84
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.25
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.96
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.72
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.70
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.05
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.88
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000050197
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.06
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999959366
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.91
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:11.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94404621.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56413
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 9                  :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 11                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5269
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.80
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    6.04
 p-value of test no 39                 :  9.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.96
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.94
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.13
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.54
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.19
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.06
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.97
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.46
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.41
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.28
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.94
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.00
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907754
   j =  2                              :            46120
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907694
   j =  2                              :            46147
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.24
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.87
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.66
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.69
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.62
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.21
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.55
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.49
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.79
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.42
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.85
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.20
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.62
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.37
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.99
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.13
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.59
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.18
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.10
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.79
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.65
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.50
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.75
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.50
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.41
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.38
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.53
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.89
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.44
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.06
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.01
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.66
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4764.82
 p-value of test no 173                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.55
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.53
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.55
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.10
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.78
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.45
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.63
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.17
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.68
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.86
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.72
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.32
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.58
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.40
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000010339
 
 Normal statistic for number of bits   :   0.082
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.92
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000013267
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:38.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2S, t = 9         9.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95420429.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56414
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.62
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     255
 p-value of test no 37                 :    0.9957
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.57
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.41
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.39
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.06
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.04
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.09
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.17
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.23
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.90
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.05
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.41
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.14
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.43
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.29
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.58
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908252
   j =  2                              :            45871
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908113
   j =  2                              :            45936
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.34
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.77
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.60
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.71
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.76
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.50
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.85
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.41
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.50
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.74
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.97
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.72
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.94
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.94
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.96
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.33
 p-value of test no 153                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.22
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.87
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.38
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.84
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.84
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.49
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.93
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.28
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.64
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.07
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.52
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.70
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.58
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.50
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.55
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.55
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.70
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.26
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.02
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.45
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.42
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   38.48
 p-value of test no 178                :  1.3e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.25
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.25
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.43
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.57
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.26
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 216                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.74
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.64
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.05
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.79
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12158.01
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.84
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.12
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999900407
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.61
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000021820
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:28.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  81  LinearComp, r = 0               1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96600077.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56415
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.28
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.72
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.77
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.64
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.21
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.04
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.61
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  182.91
 p-value of test no 54                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.07
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.16
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.93
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.02
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.80
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.33
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.28
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.17
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908347
   j =  2                              :            45819
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 116                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.28
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.00
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.73
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.52
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.73
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.45
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.26
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.42
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.92
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.58
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.42
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.97
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.28
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.48
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.06
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.86
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.47
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.40
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.72
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.44
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.28
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.71
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.09
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.76
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.41
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.01
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.59
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.75
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.11
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.89
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.66
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.61
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.51
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.97
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.12
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.21
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.91
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.02
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.18
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.96
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9754.66
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.04
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.46
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.66
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.60
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.62
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.01
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.14
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000102805
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.22
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000034636
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 248                :    0.04
 
 Sample variance                       :    2.13
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:18.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97615885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56416
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 3                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.98
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.00
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.78
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.24
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.62
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.97
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.62
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.17
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.75
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.24
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.21
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.80
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.08
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908188
   j =  2                              :            45894
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908380
   j =  2                              :            45807
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.77e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.93
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.29
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.83
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.74
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.83
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.40
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.00
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.71
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.53
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.81
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17714.61
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.81
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.78
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.76
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.34
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.43
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.58
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.89
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.65
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.80
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.48
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.12
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.45
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.59
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.36
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.88
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.22
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.36
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.52
 p-value of test no 167                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.43
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.63
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.15
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.33
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.47
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.51
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.87
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.84
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.07
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.25
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.04
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.15
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.82
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.01
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.37
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.90
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.48
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.00
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.73
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.39
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11558.97
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.33
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999943190
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999925241
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.68e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:07.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98598925.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56417
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.64
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.37
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.78
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.95
 p-value of test no 49                 :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.30
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.74
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.61
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.93
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.45
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.85
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.04
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.90
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.69
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908485
   j =  2                              :            45750
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908311
   j =  2                              :            45837
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 72                 :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 73                 :    0.9941
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.23
 p-value of test no 119                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.54
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.17
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.20
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.09
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.96
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.85
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.32
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.91
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.39
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.10
 p-value of test no 146                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.82
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.83
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.29
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.06
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.51
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.19
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.38
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.50
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.24
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.90
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.59
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.91
 p-value of test no 160                :    0.9920
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.45
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.90
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.85
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  204.53
 p-value of test no 164                :  1.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.54
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.02
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.86
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4814.84
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.33
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.27
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.70
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.80
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.04
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.02
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.03
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.27
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.54
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.46
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.48
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10249.49
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.63
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.31
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.52
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.75
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.70
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.24
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11627.11
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.36
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999988352
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.52
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000013180
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:20.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    1.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100040717.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56418
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.25
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.70
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.09
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.44
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.12
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.68
 p-value of test no 53                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.42
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.14
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.99
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.72
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.18
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.12
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.98
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.82
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908149
   j =  2                              :            45915
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908374
   j =  2                              :            45807
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 86                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.62
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.16
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.99
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.47
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.54
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.51
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.81
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.81
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.20
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.68
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.54
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.19
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.27
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.51
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.75
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.56
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.88
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.27
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.94
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.60
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.95
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.07
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.16
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.14
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.99
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.66
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.35
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.36
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.18
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.51
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.11
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.91
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.31
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.15
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.58
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.94
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.64
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.65
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.27
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.08
 p-value of test no 198                :    0.9977
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.56
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.72
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.60
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.29
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.88
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.90
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.99
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.72
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.98
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.93
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.94
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999940160
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000034018
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:57.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101122061.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56419
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4182
 p-value of test no 17                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     664
 p-value of test no 31                 :  5.3e-3
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.27
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.87
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.04
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.14
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.97
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.16
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.67
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.15
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.15
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.77
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.46
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.97
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.73
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907742
   j =  2                              :            46123
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908297
   j =  2                              :            45844
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 104                :    0.9945
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.50
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.21
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.96
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.32
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.14
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.37
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.09
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.54
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.44
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17675.21
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.70
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.02
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.17
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.76
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.90
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.82
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.02
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.02
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.15
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.68
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.75
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.56
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.16
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.15
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.95
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.41
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.15
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.08
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.82
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.72
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.55
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.46
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.07
 p-value of test no 170                :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.32
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.40
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.63
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.24
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.89
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.71
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.58
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.60
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.12
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9765.29
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.21
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.02
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.94
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.29
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11587.09
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.10
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.97
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999997949
 
 Normal statistic for number of bits   :  -0.016
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.34
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999890156
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:19.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101974029.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56420
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.00
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.92
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.89
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.81
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.07
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.27
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.23
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.02
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.38
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.97
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.27
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.65
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.69
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.40
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.25
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908752
   j =  2                              :            45615
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.22e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.96
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.34
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.08
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.13
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.31
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.44
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.36
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.33
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.34
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.68
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.15
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.93
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.23
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.49
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.23
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.00
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.15
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.86
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.51
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.32
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.07
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.11
 p-value of test no 157                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.02
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.03
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.13
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.29
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.66
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.45
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.42
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.02
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.44
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.99
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.58
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.17
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.32
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.08
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.48
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.06
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.84
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.42
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.21
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.42
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.47
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.79
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.92
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.72
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.11
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.47
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.21
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.11
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.02
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.69
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000075184
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.50
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999970106
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:55.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82280459.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56421
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9914
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 34                 :    0.9963
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.84
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.29
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.14
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.13
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.50
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.33
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.35
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1555.13
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.13
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.78
 p-value of test no 58                 :  4.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    4.74
 p-value of test no 60                 :  4.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.80
 p-value of test no 61                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.28
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.28
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.83
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.18
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46318
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870318
   j =  1                              :        399907367
   j =  2                              :            46312
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907803
   j =  2                              :            46091
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.37
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.20
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.41
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.53
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.47
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.13
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.66
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.97
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17253.30
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.78
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.84
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.23
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.62
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.74
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.55
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.82
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.79
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.49
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  609.04
 p-value of test no 158                :  5.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.43
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.06
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.95
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.99
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.41
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.82
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.71
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.66
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.82
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.45
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.76
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.89
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.14
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.50
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.16
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.98
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.65
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.82
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.47
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.47
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.11
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.24
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.91
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.48
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.55
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.37
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.14
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.92
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.92
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.54
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999926873
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.42
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000083626
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.063
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:26.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 J (L=1000, r=0)     5.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83132429.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56422
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    3.28
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.99
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.55
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.57
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.37
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.35
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.68
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.19
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.30
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.46
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.51
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.57
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.70
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908699
   j =  2                              :            45637
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908685
   j =  2                              :            45650
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 105                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.45
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.76
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.28
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.23
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.57
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.17
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.65
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.02
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.31
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.12
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.82
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.96
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.28
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.90
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.55
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.32
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.07
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.28
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.05
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.10
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.82
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.16
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.68
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.25
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.41
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.78
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.26
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.19
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.45
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.70
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.59
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.74
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.90
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.64
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.30
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.82
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.71
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.18
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.97
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.34
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9978
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.01
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.70
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.51
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.85
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.02
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.43
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.18
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.07
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.09
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.21
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.58
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11525.67
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.43
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999899054
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.81
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999894251
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:52.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84246541.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56423
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.03
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    5.16
 p-value of test no 36                 :  2.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    2.59
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.06
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.89
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.56
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.91
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.16
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.98
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.39
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.68
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.52
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.75
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.87
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.09
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.91
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.27
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.30
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4884.89
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908101
   j =  2                              :            45945
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908346
   j =  2                              :            45824
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 87                 :  1.6e-4    *****
 
 Anderson-Darling statistic = A2       :    6.53
 p-value of test no 88                 :  5.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  4.4e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.050
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.20
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.24
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.62
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.24
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.10
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.06
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.48
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.24
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.99
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.39
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.93
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.55
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.34
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.09
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.79
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.07
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.58
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.23
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.23
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.22
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.43
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.61
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.67
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.93
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.30
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.51
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.03
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.28
 p-value of test no 166                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.49
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.53
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.96
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.37
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.77
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.11
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.79
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.74
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.92
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.51
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.51
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.42
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.08
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.86
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.36
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.44
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.14
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.97
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.60
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.06
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999956075
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.94
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000123145
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:46.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  4.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85393421.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56424
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     971
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.38
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.74
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.79
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.94
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.55
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.34
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  171.48
 p-value of test no 54                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.42
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.18
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.06
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.10
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.02
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.59
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.62
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4886.45
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46244
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870244
   j =  1                              :        399907517
   j =  2                              :            46234
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46247
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870247
   j =  1                              :        399907510
   j =  2                              :            46239
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.30
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.79
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.99
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.17
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.93
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.19
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.14
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.80
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.59
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.09
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.19
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.73
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.15
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.83
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.45
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.16
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.44
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.42
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.55
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.97
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.09
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.02
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.47
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.39
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.88
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.50
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.77
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.96
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.21
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  450.09
 p-value of test no 169                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.57
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.72
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.40
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.53
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.34
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.59
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.06
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.11
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.54
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 212                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10370.62
 p-value of test no 215                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.86
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.12
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4269.86
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.09
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.45
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.85
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.90
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999964904
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.83
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999925679
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.029
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:58.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86310925.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56425
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    3.59
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.16
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.85
 p-value of test no 40                 :  1.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.03
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.53
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.56
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.46
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.09
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.94
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.65
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.79
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.61
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7427.92
 p-value of test no 57                 :  7.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.43
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.14
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.52
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.33
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.66
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908605
   j =  2                              :            45693
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907960
   j =  2                              :            46014
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.24
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.92
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.81
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.28
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.43
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.48
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.86
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.50
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.93
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.48
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.19
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.91
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.97
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.17
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.29
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.68
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.22
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.95
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.91
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.26
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.28
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.08
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.69
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.81
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.68
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.00
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.50
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.99
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.43
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.29
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.85
 p-value of test no 167                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.82
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.23
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.70
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.76
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.99
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4801.14
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.04
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.50
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.34
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.94
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 180                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    6.15
 p-value of test no 182                :  9.0e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.35
 p-value of test no 183                :    0.9996    *****
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.40
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.57
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.85
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.94
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.80
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 220                :    0.9943
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4650.26
 p-value of test no 222                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.33
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.77
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.38
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.62
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.70
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.33
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999976841
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.19
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000116629
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:53.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  37  Gap, r = 20                     7.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  82  LempelZiv, r = 0                0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87425026.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56426
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    3.34
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 30                 :    0.9988
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.02
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.55
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.59
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.98
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.43
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   90.15
 p-value of test no 51                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.75
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.71
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  282.73
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.87
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.78
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.70
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.92
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.61
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.15
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.94
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.19
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46299
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870299
   j =  1                              :        399907404
   j =  2                              :            46295
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 72                 :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.74
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.85
 p-value of test no 120                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.32
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.96
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.62
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.62
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.89
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.62
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.30
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.96
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.85
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.84
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.55
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.60
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.42
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.20
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.07
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.81
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.96
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.58
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.15
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.02
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.19
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.18
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.50
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.10
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.95
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.53
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.58
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.87
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.44
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.18
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.34
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.26
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.94
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.25
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.77
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.17
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.48
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.58
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5087.70
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.00
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.32
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.43
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.70
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12084.38
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.48
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999918209
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.26
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999991562
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.18
 p-value of test no 239                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.86
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:40.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88506370.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56427
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.61
 p-value of test no 22                 :  1.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.02
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.18
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.26
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.67
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.52
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.66
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.69
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.13
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.98
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.26
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.83
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.47
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.89
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.20
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46143
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870143
   j =  1                              :        399907717
   j =  2                              :            46137
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 84                 :  1.9e-3
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 85                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.45
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.24
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.96
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.88
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.22
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.37
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.01
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.03
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.49
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.59
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.82
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.99
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.50
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.85
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.97
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.21
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.58
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.59
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.94
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.68
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.55
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.82
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.75
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.03
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.32
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.13
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.55
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.76
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.61
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.41
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.57
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.67
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.00
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.13
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.92
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.89
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.28
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.44
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.81
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.79
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9956
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.58
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.41
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.53
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.43
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.95
 p-value of test no 217                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.16
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.36
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.05
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.26
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12133.91
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.38
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000008692
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.41
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000041098
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 248                :    0.9930
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 250                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.0e-3
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 253                :  8.3e-3
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:16.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89456642.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56428
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 24                 :    0.9977
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.74
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.53
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.65
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.76
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.38
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.92
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.81
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.26
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6804.88
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.96
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.63
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.79
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.33
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908037
   j =  2                              :            45974
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908683
   j =  2                              :            45651
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 74                 :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9987
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 84                 :    0.9915
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.76
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.76
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.66
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.35
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.99
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.88
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.81
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.62
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.33
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.62
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.43
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.01
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.58
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.61
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.80
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.46
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.68
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.70
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.62
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.72
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.07
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.78
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.15
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.38
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.20
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.94
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.34
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.55
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.68
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.72
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.22
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.82
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.87
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.38
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.83
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.40
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.97
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.27
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.91
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.40
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.46
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.78
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.72
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 213                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    5.72
 p-value of test no 214                :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10460.73
 p-value of test no 215                :  6.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.10
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.46
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.57
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.09
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.51
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12173.56
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.31
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000020746
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.56
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000006607
 
 Normal statistic for number of bits   :   0.052
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:46.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  91  HammingWeight2, r = 27          6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90537986.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56429
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.89
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.19
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.24
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.13
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.24
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.55
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.75
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.67
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-3
 p-value of test no 58                 :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.28
 p-value of test no 61                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.55
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.76
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.61
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5195.06
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907941
   j =  2                              :            46022
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908086
   j =  2                              :            45954
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.17
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.37
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.35
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.86
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.42
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.69
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.28
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.33
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.28
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.40
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.35
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.68
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.04
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.45
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.95
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.32
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.36
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.62
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.68
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.34
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.17
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.39
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.10
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.43
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.23
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.64
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.58
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.27
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.34
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.57
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.75
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.85
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.66
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.87
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.90
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.17
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.16
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.82
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.04
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.97
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.77
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.98
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.26
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10184.88
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.78
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.09
 p-value of test no 216                :  9.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.62
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.66
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.03
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.18
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.79
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.74
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.58
 p-value of test no 231                :    0.9936
 
 
 -----------------------------------------------
 Total number of bits:  8000024751
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.56
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999985871
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:26.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  92  HammingCorr, L = 30             9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91553794.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56430
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 5                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    5.19
 p-value of test no 39                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.91
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.39
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.07
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.41
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.69
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.82
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.13
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.02
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.75
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.72
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.37
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.24
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.42
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.33
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907726
   j =  2                              :            46134
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907953
   j =  2                              :            46019
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 73                 :    0.9945
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.69
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.61
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.72
 p-value of test no 121                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.36
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.60
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.70
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.52
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.35
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.28
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.95
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17215.08
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.67
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.74
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.36
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.80
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.78
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   56.87
 p-value of test no 153                :  2.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.98
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.99
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.68
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.13
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.63
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  115.04
 p-value of test no 160                :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.09
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.95
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.72
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.40
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.52
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.18
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.97
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4789.14
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.46
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.56
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.77
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.42
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.44
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.79
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.85
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.47
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.72
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    2.15
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.05
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.99
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.91
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.16
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.41
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.03
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.19
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.75
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.39
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.30
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.67
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.40
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999972350
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.54
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999925781
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      2.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92635138.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56431
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 3                  :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 23                 :    0.9969
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    4.81
 p-value of test no 26                 :  3.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.42
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.77
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.06
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.00
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.85
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.35
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.27
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.82
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.81
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.10
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.34
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.57
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908511
   j =  2                              :            45743
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908067
   j =  2                              :            45959
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-3
 p-value of test no 86                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 87                 :  1.2e-3
 
 Anderson-Darling statistic = A2       :    5.88
 p-value of test no 88                 :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  2.2e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-3
 p-value of test no 98                 :    0.9989
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.040
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.70
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.09
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.85
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.07
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.39
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.12
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.82
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.68
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.47
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.69
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17764.54
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.00
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.43
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.18
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.69
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.50
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.44
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.84
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.80
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.94
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.43
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.85
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.81
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.99
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.44
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.64
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.91
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.29
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.94
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.65
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.56
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.03
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.06
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.41
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.15
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.27
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.64
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.52
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.71
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.63
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.81
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.48
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.94
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 214                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10363.62
 p-value of test no 215                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.33
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.76
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.56
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.11
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.69
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.42
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.66
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000091039
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.47
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000128785
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:15.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  2.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93650946.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56432
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1200
 p-value of test no 11                 : 1 -  3.1e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334320
   j =  1                              :        599997600
   j =  2                              :             1200
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    4.21
 p-value of test no 44                 :  6.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.76
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.90
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.94
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.55
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.19
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.67
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.45
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.66
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.31
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.39
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.45
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.42
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.48
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.43
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.16
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46163
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870163
   j =  1                              :        399907680
   j =  2                              :            46151
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908000
   j =  2                              :            46000
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.78
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.61
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.57
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.04
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.80
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.65
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.60
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.90
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.73
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.61
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17605.56
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.24
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.32
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.05
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.61
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.60
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.61
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.00
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.89
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.90
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.35
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.23
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.06
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.08
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.79
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.23
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.59
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.29
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.39
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.50
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.20
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.63
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.44
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.73
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.75
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.04
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.00
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.33
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.82
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.08
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.38
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.21
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9766.72
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.37
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.43
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.30
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.87
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.77
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.41
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.93
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.28
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999903434
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.07
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999927524
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:28.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  3.1e-6
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94699522.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56433
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.29
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.58
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.93
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.62
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.02
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.22
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.88
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.21
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.47
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7330.78
 p-value of test no 57                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.05
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.49
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.53
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.76
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.84
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908078
   j =  2                              :            45958
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907777
   j =  2                              :            46107
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
 p-value of test no 100                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.72
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.79
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.52
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.90
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.46
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.36
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.53
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.16
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.80
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.65
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17579.54
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.78
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.37
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.61
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.41
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.58
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.55
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.60
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.54
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.46
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.34
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.98
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.45
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.59
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.90
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.77
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.86
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.98
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.79
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.41
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.01
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.58
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.57
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.61
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.50
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.27
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.40
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.28
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.45
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.52
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.39
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.13
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.69
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.65
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10255.28
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.86
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.47
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.11
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.70
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.69
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12053.21
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.93
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.97
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000039628
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.24
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999954644
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 238                :    0.06
 
 Sample variance                       :    2.70
 p-value of test no 239                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 253                :    0.13
 
 Sample variance                       :    2.02
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:37.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95551489.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56434
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 11                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.84
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.59
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.30
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.60
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.17
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.86
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.41
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.05
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.35
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.90
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.95
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.12
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.01
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.30
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4944.62
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45325
 p-value of test no 70                 :    0.9952
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869325
   j =  1                              :        399909353
   j =  2                              :            45319
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908119
   j =  2                              :            45936
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.46
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.76
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.55
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.32
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.50
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.18
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.38
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.72
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.45
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17281.23
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.45
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.50
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.75
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.87
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.29
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.36
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.79
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.09
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.79
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.67
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.90
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.85
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.68
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.12
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.66
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.33
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.78
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.11
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.82
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.78
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.72
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.71
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.21
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.56
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.25
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4774.84
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.76
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.41
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.40
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.44
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.18
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.94
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.21
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.29
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5144.64
 p-value of test no 222                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.39
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4415.72
 p-value of test no 227                :  6.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.72
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.54
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.86
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.92
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000075022
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.40
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000038704
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    2.10
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-3
 p-value of test no 246                :    0.9982
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.79
 p-value of test no 248                :    0.9973
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:58.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  97  HammingIndep, L=300, r=0        6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96796673.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56435
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5280
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.80
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.29
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.09
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.19
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.05
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.70
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.90
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.10
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.76
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.46
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.55
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.62
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908846
   j =  2                              :            45577
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908050
   j =  2                              :            45972
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.80
 p-value of test no 117                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.34
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.49
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.37
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.33
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.45
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.97
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.37
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.60
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.25
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17020.61
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.43
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.23
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.35
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.04
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.15
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.07
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.74
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.98
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.84
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.63
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.29
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.87
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.37
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.73
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.27
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.22
 p-value of test no 165                :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.38
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5208.29
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.98
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.20
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.67
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.73
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.43
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.26
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.94
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.19
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.12
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.44
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.68
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.39
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.85
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5088.99
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.87
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.91
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.41
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.38
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.08
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.01
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999970604
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.86
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000018457
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:36.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97845249.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56436
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.76
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.55
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.99
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.19
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.28
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.35
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.17
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.19
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6838.31
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.08
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.11
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.96
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.05
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.79
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908339
   j =  2                              :            45829
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908518
   j =  2                              :            45735
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.18
 p-value of test no 115                :  7.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.30
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.75
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.22
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.67
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.60
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.91
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.30
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.52
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.26
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.46
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.19
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.76
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.76
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.29
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.96
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.98
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.59
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.74
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.80
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.83
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.12
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.78
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.02
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.32
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.87
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.13
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.08
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.73
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.99
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.45
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.27
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.60
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.81
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.35
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.06
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.53
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.17
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.89
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.05
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.44
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.64
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.85
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.93
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4291.79
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.28
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.24
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.51
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999887282
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.10
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000095512
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:05.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  55  SampleCorr, k = 1               7.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98828289.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56437
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 26                 :    0.9973
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.04
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.36
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.81
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.11
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.74
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.31
 p-value of test no 50                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.34
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.27
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.95
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.93
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6894.11
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.60
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.78
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.50
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.29
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.22
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46402
 p-value of test no 70                 :  7.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870402
   j =  1                              :        399907198
   j =  2                              :            46398
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907728
   j =  2                              :            46127
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.29
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.26
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.23
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.43
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.17
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.01
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.02
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 138                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    5.17
 p-value of test no 140                :  2.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   85.01
 p-value of test no 141                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17295.46
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.17
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.46
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.36
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.38
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.71
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.18
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.90
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.45
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.62
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  197.03
 p-value of test no 159                :  4.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.90
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.96
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.86
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.31
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.33
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.66
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.14
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.55
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.02
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.99
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.88
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.30
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.06
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.32
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.91
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.60
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.49
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
 p-value of test no 181                :    0.9953
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.05
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.00
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.74
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9747.80
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.91
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 221                :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4645.48
 p-value of test no 222                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.54
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.90
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.17
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.83
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.71
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.76
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000053230
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.47
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999860189
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:15.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          0.9992 
  76  RandomWalk1 R (L=1000, r=0)     4.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99876865.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56438
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7548
 p-value of test no 18                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7097
 p-value of test no 19                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    2.95
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    3.48
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    4.71
 p-value of test no 33                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.50
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.97
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.46
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.24
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.01
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.64
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.63
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.93
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1293.78
 p-value of test no 56                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.96
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.99
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.90
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.35
 p-value of test no 66                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.16
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.38
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908830
   j =  2                              :            45579
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908156
   j =  2                              :            45910
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.00
 p-value of test no 119                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.96
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.12
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.26
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.60
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.69
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.42
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.87
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.44
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.76
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.50
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.84
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.96
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.28
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.29
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.62
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.05
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.61
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.61
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.42
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.61
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.33
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.78
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.17
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.96
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.05
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.29
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.58
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.15
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.83
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.12
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.57
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.61
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.84
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.93
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.41
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.55
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.00
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.80
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.25
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.85
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.85
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.56
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.18
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.99
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.48
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.22
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.10
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.19
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000078022
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.22
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000034447
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:07.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100794369.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56439
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.57
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.40
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.04
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.20
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.50
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.46
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.20
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.28
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.06
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.63
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.76
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.42
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.89
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.41
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908306
   j =  2                              :            45838
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46151
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870151
   j =  1                              :        399907701
   j =  2                              :            46145
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.00
 p-value of test no 119                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.96
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.92
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.25
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.89
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.82
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.91
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17374.09
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.74
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.72
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.55
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.27
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.26
 p-value of test no 150                :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.16
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.84
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.19
 p-value of test no 153                :  2.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.01
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.46
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.07
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.22
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.05
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.61
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.82
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.42
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.32
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.08
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.76
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.48
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.35
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.08
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.01
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.84
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.16
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.34
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.97
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.77
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.52
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.48
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.91
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.02
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.31
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.94
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.00
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.14
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.84
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.74
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.95
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.34
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.00
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.50
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.98
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.53
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000060148
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.55
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999913361
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:05.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101711873.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56440
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997167
   j =  2                              :             1415
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.33
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.15
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.54
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.74
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.64
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.59
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.14
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7211.57
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.01
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.11
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.51
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.37
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908244
   j =  2                              :            45878
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907820
   j =  2                              :            46084
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 98                 :    0.9954
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.19
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.91
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.97
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   74.72
 p-value of test no 123                :  2.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.94
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.75
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.60
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.16
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.10
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.95
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.72
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.63
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.66
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.88
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.20
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.73
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.62
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.35
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.49
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.90
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.22
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.81
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.83
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.63
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.49
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.79
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.32
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.17
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.79
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.17
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.59
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.25
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.41
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.88
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.78
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.57
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.07
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.50
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.55
 p-value of test no 196                :    0.9918
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.84
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.20
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.00
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.04
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.66
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.65
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.83
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.10
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.73
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.68
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.06
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.70
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999916274
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.97
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999944624
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:45.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           2.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82313228.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56441
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4200
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.85
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.88
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.10
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.31
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.15
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.51
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.48
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.18
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.81
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.84
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.91
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.52
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.05
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.43
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.44
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.81
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.17
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.09
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907968
   j =  2                              :            46007
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46185
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907632
   j =  2                              :            46181
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-4
 p-value of test no 72                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 94                 :    0.9914
 
 Anderson-Darling statistic = A2       :    4.92
 p-value of test no 95                 :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9990
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.44
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.89
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.35
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.15
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.80
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.30
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.75
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.73
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.79
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.43
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.19
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17778.11
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.77
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.96
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.66
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.44
 p-value of test no 152                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.03
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.02
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.72
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.89
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.80
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.67
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.97
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.41
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.10
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.74
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.84
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.07
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.31
 p-value of test no 165                :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.69
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.28
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.13
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.98
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.24
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.06
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.27
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.30
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.78
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.22
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.27
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.13
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.44
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.60
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.19
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.05
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 212                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10295.38
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.82
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.84
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.45
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.02
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.13
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.62
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.55
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999827747
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.14
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999895622
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.22
 p-value of test no 244                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:39.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83853324.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56442
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.74
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.87
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.89
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.87
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.94
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.03
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.36
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1321.48
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.06
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.98
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.87
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.78
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.63
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908425
   j =  2                              :            45783
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46114
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870114
   j =  1                              :        399907774
   j =  2                              :            46110
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.14
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.69
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.60
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.56
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.04
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.38
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.31
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.31
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.70
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.68
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.38
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.92
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.87
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.01
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.70
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.25
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.69
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.58
 p-value of test no 155                :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.18
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.47
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.58
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.84
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.79
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.24
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.43
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.59
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.94
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.49
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.36
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.01
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.27
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.88
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.34
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.90
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.47
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.78
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.75
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.05
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.39
 p-value of test no 178                :    0.9921
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
 p-value of test no 180                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.20
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.18
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.82
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.48
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.73
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.09
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4278.18
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.27
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.62
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.26
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.05
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000065023
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.39
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999944135
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    3.25
 p-value of test no 244                :  5.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    4.84
 p-value of test no 247                :  3.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.81
 p-value of test no 248                :  2.5e-3
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:07.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84738060.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56443
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 12                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.84
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.22
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.89
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.32
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.76
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.69
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6734.53
 p-value of test no 57                 :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.54
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.96
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.72
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.63
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4833.14
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908463
   j =  2                              :            45764
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908279
   j =  2                              :            45856
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.8e-3
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.59
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.85
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.73
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.69
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.77
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.60
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.68
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.81
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.27
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.16
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.28
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17652.07
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.73
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.01
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.34
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.84
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.23
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.60
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.15
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.63
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.01
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.14
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.49
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.77
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.99
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.13
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.77
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.56
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.14
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.69
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.34
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.40
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.69
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.51
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.78
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.89
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.53
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.09
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.97
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.26
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.98
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.25
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.57
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.68
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.98
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.92
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.47
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.95
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.45
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.87
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.57
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   88.80
 p-value of test no 231                :  2.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000093343
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.78
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999936821
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9951
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:28.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85655564.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56444
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.59
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.04
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.69
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.10
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.60
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.39
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.96
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.80
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.20
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.89
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.86
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.51
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.71
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5242.79
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908697
   j =  2                              :            45650
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908216
   j =  2                              :            45886
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.36
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.43
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.54
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.68
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.64
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.77
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.52
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.53
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.75
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.34
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.44
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.67
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.88
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.09
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.61
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.16
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.71
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.62
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.33
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.31
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.75
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.64
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.42
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.74
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.47
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.92
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.83
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.04
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.37
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.24
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.43
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.45
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.18
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.58
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.49
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.23
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.52
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.68
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.86
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.37
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.90
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 208                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10301.76
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.65
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.28
 p-value of test no 217                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.76
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.30
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.13
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.42
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.96
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.41
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.10
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000013000
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.95
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999988400
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:35.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  93  HammingCorr, L = 300            0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86704140.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56445
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.11
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   41.11
 p-value of test no 49                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.94
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.84
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.57
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.42
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.69
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.01
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.81
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.20
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.07
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.97
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.20
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.54
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908176
   j =  2                              :            45909
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908264
   j =  2                              :            45862
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.52
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.14
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.88
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.85
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.33
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.95
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.60
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.55
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.68
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.84
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.27
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.06
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.72
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.34
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.77
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.02
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.73
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.61
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.11
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.48
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.19
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.91
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.17
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.23
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.52
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.03
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.87
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.43
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.05
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.79
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.22
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.75
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.80
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.96
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.45
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.42
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.17
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.89
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.25
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.17
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.75
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.79
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.08
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.38
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.05
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.81
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.75
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.88
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.61
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.31
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.70
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.38
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000042199
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.13
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999860726
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:00.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87687180.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56446
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 10                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 24                 :    0.9969
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 35                 :    0.9961
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.54
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.06
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.72
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.31
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.91
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.96
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.77
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  4.8e-3
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 60                 :  5.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.68
 p-value of test no 61                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.40
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.75
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5186.96
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46065
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907872
   j =  2                              :            46061
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908832
   j =  2                              :            45575
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.66
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.95
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.84
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.07
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.56
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.42
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.23
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.87
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.25
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.25
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17116.37
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.82
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.28
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.64
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.03
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.49
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.21
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.44
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.57
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.24
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.10
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.34
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.04
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.16
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.07
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.82
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.90
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.76
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.18
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.00
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.53
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.27
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.00
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.39
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.01
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.67
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.21
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.88
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.64
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.94
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.81
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.25
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.26
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.99
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.46
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.57
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.16
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.14
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.82
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.61
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.70
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.52
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.34
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000048865
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.20
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999914183
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:20.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88604684.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56447
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7539
 p-value of test no 20                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.31
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.07
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.53
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.76
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.43
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.29
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.94
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.54
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1547.09
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.02
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.07
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.51
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.41
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.32
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907626
   j =  2                              :            46181
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908248
   j =  2                              :            45870
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-4
 p-value of test no 110                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-5
 p-value of test no 113                :    0.9955
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  107.87
 p-value of test no 119                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.23
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.10
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.58
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.07
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.68
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.92
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.58
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.04
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17780.55
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.41
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.71
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.21
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.99
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.53
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.47
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.07
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.78
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.83
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.95
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.37
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.96
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.23
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.34
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.18
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.37
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.02
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.84
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.67
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.16
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.94
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.22
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.05
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.60
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.23
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.40
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.09
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.64
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.11
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.11
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10230.09
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10315.55
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.86
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.61
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.49
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.78
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.45
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.99
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.84
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000126109
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.86
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999912374
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:47.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89522201.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56448
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.48
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.21
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.02
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.82
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.00
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.05
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.25
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.37
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.83
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.71
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.14
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.05
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.14
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.98
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.10
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.94
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.76
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908245
   j =  2                              :            45870
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45539
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908925
   j =  2                              :            45533
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.85
 p-value of test no 117                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.24
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.78
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.56
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.47
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.15
 p-value of test no 123                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.56
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.49
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.55
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.39
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.25
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.07
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.52
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.94
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.05
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.71
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.77
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.46
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.32
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.38
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.59
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   98.74
 p-value of test no 156                :    0.9990    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.74
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.10
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.31
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.03
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.48
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.38
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.04
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.45
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.33
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.55
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.96
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.80
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  311.35
 p-value of test no 169                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.06
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.17
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.19
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.60
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.89
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.18
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.08
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-4
 p-value of test no 194                :    0.9947
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.59
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.21
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.12
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.34
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.23
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.20
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.83
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.88
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.58
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.95
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.60
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.26
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.61
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999902210
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999887600
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.17
 p-value of test no 249                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:55.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     0.9990 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90505241.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56449
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.86
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.48
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.76
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.47
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.61
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.85
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.62
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.60
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1332.68
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.47
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.50
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.04
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.31
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.39
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.01
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908266
   j =  2                              :            45861
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908461
   j =  2                              :            45759
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.07
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.80
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.43
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.52
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.93
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.79
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.29
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.42
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.38
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.46
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.60
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.30
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.57
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.43
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.92
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.50
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.63
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.02
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.57
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.73
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.49
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.62
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.81
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.77
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.57
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.18
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.62
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.10
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.56
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.49
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.38
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.82
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.96
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.23
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.60
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.97
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.83
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.86
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.71
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.26
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.48
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.99
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.00
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9751.87
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.49
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.07
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.10
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.53
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.82
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.51
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000156562
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.73
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999997298
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:22.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91455513.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56450
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997316
   j =  2                              :             1339
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9952
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    4.08
 p-value of test no 26                 :  7.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9921
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.96
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.92
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.76
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.12
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.71
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.77
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.15
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.69
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.60
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.36
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.19
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.75
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.54
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45479
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869479
   j =  1                              :        399909045
   j =  2                              :            45473
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46302
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870302
   j =  1                              :        399907399
   j =  2                              :            46296
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.91
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.72
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.19
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.22
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.94
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.11
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.33
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.49
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.65
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.93
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.05
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.73
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.08
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.10
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.13
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.57
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.80
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.09
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.46
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.91
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.21
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.50
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.11
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.85
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.58
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.28
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.58
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.93
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.70
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.18
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.95
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.82
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.96
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.17
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.71
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.14
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.52
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.96
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.20
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.67
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.35
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.73
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.13
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.41
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.62
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.72
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.82
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.58
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12089.73
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.29
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.16
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999969860
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.26
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000035608
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:33.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92405785.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56451
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 18                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    3.77
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.75
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.61
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.48
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.65
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.00
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.44
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.49
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.19
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.29
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6851.40
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.37
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.50
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.53
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.58
 p-value of test no 67                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.93
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908300
   j =  2                              :            45847
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908163
   j =  2                              :            45914
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.33
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.67
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.19
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.50
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.25
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.71
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.69
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.38
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.17
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.60
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.96
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.77
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.22
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.31
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.76
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.01
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.82
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.59
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.55
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.07
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.18
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.91
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.55
 p-value of test no 159                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.37
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.77
 p-value of test no 161                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.94
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.56
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.12
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.61
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.46
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.22
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.01
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.19
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.02
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.58
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.60
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.81
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.17
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.87
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.07
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.22
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.70
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.73
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.62
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.22
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.80
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.83
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.25
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.25
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3909.14
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.17
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11553.76
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.02
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.01
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999887582
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000167479
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:47.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93913113.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56452
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.37
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.92
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.42
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.32
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.23
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.97
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6761.78
 p-value of test no 57                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.90
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
 p-value of test no 62                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.61
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.54
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.59
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907826
   j =  2                              :            46084
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45557
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869557
   j =  1                              :        399908893
   j =  2                              :            45543
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 102                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.08
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.69
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.21
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.52
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.18
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.55
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.00
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.60
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.19
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17039.65
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.65
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.94
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.53
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.07
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.11
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.68
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.66
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.73
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.39
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.40
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.17
 p-value of test no 161                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.67
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.59
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.09
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.51
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.51
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.48
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.05
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.35
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.48
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.79
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.87
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.33
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.04
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.41
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.28
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.49
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.73
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.06
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.37
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.46
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.21
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.14
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.84
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.58
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.00
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.30
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12209.37
 p-value of test no 230                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.70
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000094975
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.73
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999927407
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:45.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95092761.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56453
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    3.78
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.39
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.80
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.73
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.05
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.69
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.67
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.32
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.36
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.65
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.43
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.35
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.85
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.79
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.77
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.06
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.24
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908057
   j =  2                              :            45961
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908138
   j =  2                              :            45928
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-3
 p-value of test no 72                 :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.70
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.37
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.64
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.21
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.80
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.84
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.83
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.40
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.10
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17230.23
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.56
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.44
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.43
 p-value of test no 149                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.82
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.80
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.10
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.36
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.23
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.86
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.47
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.00
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.30
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.13
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.08
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.83
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.38
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.83
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.85
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.75
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.73
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.05
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.74
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.67
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.70
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.65
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.59
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.59
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.91
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.45
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.45
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.91
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.54
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.20
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.48
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.08
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12275.57
 p-value of test no 229                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.36
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.47
 p-value of test no 231                :  9.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000078532
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.23
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999901502
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    2.87
 p-value of test no 244                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:59.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96108569.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56454
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     823
 p-value of test no 25                 :    0.9951
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.9902
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.56
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.14
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.67
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.37
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.27
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.09
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.72
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.35
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.06
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.85
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.77
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.18
 p-value of test no 67                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.97
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908575
   j =  2                              :            45702
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907897
   j =  2                              :            46047
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.48
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.13
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.87
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.79
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.06
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.54
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.19
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.85
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 139                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.13
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.03
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.78
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.95
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.56
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.57
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.37
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.20
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.87
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.45
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.06
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.53
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.05
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.10
 p-value of test no 157                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.59
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.78
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.64
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.91
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.56
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.60
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.85
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.83
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.09
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.39
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.77
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.47
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.37
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.03
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.76
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.46
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.90
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.20
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.91
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.93
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.71
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.56
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.81
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.05
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4706.67
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.10
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.52
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.11
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.05
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.32
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.94
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000011167
 
 Normal statistic for number of bits   :   0.088
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.97
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999886709
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:10.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97091609.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56455
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.72
 p-value of test no 48                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.22
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.10
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.54
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.49
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.94
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.21
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6882.67
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.84
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.36
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.29
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.80
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.99
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908805
   j =  2                              :            45593
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908304
   j =  2                              :            45842
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.71e-4
 p-value of test no 109                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.38
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.67
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.40
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.47
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.34
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.61
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.58
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.52
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.43
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.79
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.14
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.69
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.38
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.74
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.63
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.50
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.22
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.13
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.74
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.92
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.74
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.19
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.43
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.06
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.86
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.18
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.25
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.91
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.86
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.82
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.81
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.60
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.10
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.17
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.96
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.08
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.59
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.63
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.14
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.33
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.82
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.86
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.43
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
 p-value of test no 204                :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.69
 p-value of test no 207                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.96
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.33
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.38
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.88
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.37
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.53
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11487.34
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.46
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.67
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999993671
 
 Normal statistic for number of bits   :  -0.050
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.54
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000056863
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:13.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98107417.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56456
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5631
 p-value of test no 13                 :  2.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    4.60
 p-value of test no 33                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.67
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.19
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.58
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.88
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.94
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.55
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.71
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.00
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1342.25
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.07
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.53
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.35
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.25
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.39
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908586
   j =  2                              :            45701
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908148
   j =  2                              :            45920
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
 p-value of test no 107                :    0.9972
 
 Anderson-Darling statistic = A2       :    5.61
 p-value of test no 108                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-6
 p-value of test no 113                :    0.9972
 
 Anderson-Darling statistic = A2       :    3.89
 p-value of test no 114                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.45
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.83
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.12
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.67
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.81
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.01
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.09
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.72
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.11
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.87
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.88
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.77
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.66
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.26
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.26
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.10
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.41
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.84
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.80
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.19
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.38
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.91
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.76
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.41
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.80
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.87
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.31
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.05
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.45
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.10
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.56
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.19
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.66
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.20
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.47
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 186                :    0.9918
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 188                :    0.9916
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.44
 p-value of test no 198                :    0.9937
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.96
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.61
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10297.59
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9793.46
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.30
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.10
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.86
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.44
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.50
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.31
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.62
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.90
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999990728
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.64
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999877376
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:20.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99090457.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56457
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.44
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.15
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.33
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.40
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.77
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.42
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.33
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.23
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.63
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.80
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.79
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908252
   j =  2                              :            45868
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908406
   j =  2                              :            45788
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
 p-value of test no 77                 :    0.9983
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.30
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.91
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.44
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.81
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.58
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.22
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.95
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17703.45
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.77
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.74
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.69
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.85
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.95
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.77
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.37
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.93
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.20
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.25
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.56
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.22
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.69
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.27
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.76
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.53
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.48
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.34
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.59
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.86
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.96
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.33
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.66
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.73
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.79
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.49
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.67
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.82
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.81
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.58
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.29
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.28
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.83
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4677.70
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.73
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.02
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.56
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.99
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.84
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.96
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000071155
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.81
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000112234
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:09.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100171801.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56458
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  8.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    2.94
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.72
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.15
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.01
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.04
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.99
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.93
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.89
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.63
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.84
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.04
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.77
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.83
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.12
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908154
   j =  2                              :            45920
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908524
   j =  2                              :            45729
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 88                 :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9974
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.99
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.99
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.28
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.35
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.59
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.78
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.22
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.92
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.50
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17301.57
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.54
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.10
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.75
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.81
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.33
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.60
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.85
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.67
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.93
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.87
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.86
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.78
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.17
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.85
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.94
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.45
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.38
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.48
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.59
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.10
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.13
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.24
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.56
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.21
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.10
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.05
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.88
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.15
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.72
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.34
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.51
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10267.61
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.84
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.21
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3916.73
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.98
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.37
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.63
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.67
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999996410
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.91
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000280648
 
 Normal statistic for number of bits   :    2.22
 p-value of test no 234                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:57.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               8.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101089305.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56459
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.83
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.83
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.44
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.53
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.45
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.13
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.96
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.92
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.05
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.09
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.11
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.31
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.45
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908032
   j =  2                              :            45975
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908012
   j =  2                              :            45991
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.43
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.64
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.57
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.21
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.21
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.21
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.05
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.54
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.54
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.79
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.38
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.99
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.02
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.76
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.54
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.02
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.93
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.65
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.07
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.83
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.20
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.44
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.73
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.54
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.08
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.94
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.85
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.56
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.12
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.14
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.33
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.98
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.77
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5230.78
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.04
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.66
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.30
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.03
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.90
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10286.41
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
 p-value of test no 212                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10253.45
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.67
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.16
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.07
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.21
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.88
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12129.59
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.04
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000053893
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.96
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999939977
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:40.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102203417.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56460
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 12                 :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    3.88
 p-value of test no 24                 :  9.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     971
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.73
 p-value of test no 29                 :  4.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.14
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.11
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.96
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.97
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.84
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.89
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.85
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.87
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1288.19
 p-value of test no 56                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.97
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.43
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.18
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.72
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.39
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46148
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870148
   j =  1                              :        399907708
   j =  2                              :            46140
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45557
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869557
   j =  1                              :        399908889
   j =  2                              :            45551
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  104.61
 p-value of test no 120                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.35
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.03
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.68
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.71
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.41
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 142                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 144                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16928.09
 p-value of test no 145                :    0.9966
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.12
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.40
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.31
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.71
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.82
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.90
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.71
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.39
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.50
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.74
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.28
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.29
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.53
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.84
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.33
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.19
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.91
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.27
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.52
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.76
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.26
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.67
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.08
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.73
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.52
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.15
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.46
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.20
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.68
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.60
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.74
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.52
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.06
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.97
 p-value of test no 218                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.85
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.69
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.14
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.73
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.39
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.57
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.21
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999885248
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.05
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000057334
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:53.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82345997.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56461
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 4                  :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5638
 p-value of test no 13                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    5.50
 p-value of test no 27                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     538
 p-value of test no 31                 :    0.9946
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.20
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.32
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.52
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.40
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.57
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.44
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.51
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.73
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.77
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7279.30
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.72
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.06
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.08
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.03
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.81
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907928
   j =  2                              :            46030
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908441
   j =  2                              :            45775
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 101                :  5.8e-3
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.50
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.97
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.79
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.76
 p-value of test no 122                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.16
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.38
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.59
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.80
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.77
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17928.12
 p-value of test no 145                :  4.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.36
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.41
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.98
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.56
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.59
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.77
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.43
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.36
 p-value of test no 153                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.48
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.19
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.01
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.42
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.31
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.34
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.45
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   94.00
 p-value of test no 161                :    0.9997    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.70
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.67
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.29
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.70
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.48
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.01
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.56
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.76
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.37
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.95
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.39
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.79
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.04
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.53
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.95
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    2.16
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.59
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.50
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.40
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.87
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10222.00
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.45
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.26
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.70
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.63
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.43
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12329.81
 p-value of test no 229                :  5.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.38
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   90.14
 p-value of test no 231                :  1.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999870917
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.45
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999890252
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 253                :    0.49
 
 Sample variance                       :    3.04
 p-value of test no 254                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:37.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  99  HammingIndep, L=1200, r=0       5.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83099659.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56462
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.97
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.49
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.26
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.48
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.11
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.82
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.53
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.92
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.28
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.79
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.27
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.15
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.82
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.38
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908418
   j =  2                              :            45788
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907823
   j =  2                              :            46081
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.29
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.12
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.43
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.12
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.70
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.27
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.13
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.14
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.97
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.72
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.24
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.30
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.41
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.32
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.96
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.06
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.64
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.88
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.04
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.00
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.65
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.26
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.30
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.14
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.49
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.01
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.83
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.08
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.31
 p-value of test no 164                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   39.18
 p-value of test no 165                :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.39
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.30
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.91
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.61
 p-value of test no 169                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.68
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.75
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.63
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.21
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.50
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.88
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.02
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.87
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.63
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.27
 p-value of test no 207                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.55
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.76
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.94
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.69
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.85
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.62
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.17
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.86
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.99
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000018193
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.78
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999972743
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:20.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84803595.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56463
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.26
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.34
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.33
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.34
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.49
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.49
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.02
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6796.14
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.76
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.04
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.84
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.84
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908013
   j =  2                              :            45989
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908166
   j =  2                              :            45911
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-4
 p-value of test no 84                 :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 85                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.11
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.57
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.39
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.12
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.73
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.12
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.28
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.82
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.62
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.61
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17266.84
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.92
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.60
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.07
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.60
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.86
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.00
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.64
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.24
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.21
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.13
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.20
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.11
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.78
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.01
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.10
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.09
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.83
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.03
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.26
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.42
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.96
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.76
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.35
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.78
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.79
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.63
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.31
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.57
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.35
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.18
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.75
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.07
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.61
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.27
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.64
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.23
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.90
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.03
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.46
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.72
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.29
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000009985
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.79
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000027964
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:03.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85721099.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56464
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.71
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.15
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.93
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.63
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.77
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.45
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.06
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.75
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.50
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.26
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.17
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.35
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908423
   j =  2                              :            45784
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908140
   j =  2                              :            45924
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.84
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.20
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.16
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.37
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 128                :  8.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.41
 p-value of test no 129                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.06
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.48
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17602.28
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.11
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.18
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.49
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.94
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.36
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.63
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.59
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.48
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.75
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.87
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.57
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.60
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.72
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.01
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.16
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.56
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.95
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.98
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.25
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.77
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.82
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.22
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.88
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.44
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.78
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.83
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.64
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.31
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.78
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.16
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 212                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 214                :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9612.20
 p-value of test no 215                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.62
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.84
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.69
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.09
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.68
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.53
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.04
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000059968
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.92
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999985862
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:14.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86671371.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56465
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    3.08
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.02
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.49
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.04
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.63
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.08
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.78
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.65
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.89
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7218.34
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.05
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.21
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.20
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.08
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46387
 p-value of test no 70                 :  9.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870387
   j =  1                              :        399907229
   j =  2                              :            46381
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907981
   j =  2                              :            46008
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.00
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.48
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.37
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.95
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.32
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.91
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.19
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.72
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.72
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.92
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.11
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.08
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.43
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.88
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.70
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.84
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.38
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.14
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.78
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.53
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.37
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.63
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.39
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.54
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.90
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.02
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.64
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.38
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.01
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  469.88
 p-value of test no 166                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.58
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.22
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.69
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.82
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.32
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.62
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5178.16
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.22
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.48
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.56
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.65
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.94
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.40
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.26
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.72
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.76
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.71
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.42
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.04
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.42
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.88
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12165.47
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.38
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999895019
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999931643
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:17.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87654411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56466
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 7                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5241
 p-value of test no 13                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 39                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.02
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.59
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.21
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.48
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.30
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.35
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1332.48
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.47
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.19
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.18
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.40
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.09
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907821
   j =  2                              :            46076
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908309
   j =  2                              :            45844
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-4
 p-value of test no 112                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-6
 p-value of test no 113                :    0.9969
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 114                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.97
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.68
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.03
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.11
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.51
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.63
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.73
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.44
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.13
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.69
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.87
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.07
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.48
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.14
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.56
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.49
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.15
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.95
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.76
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.77
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.93
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.96
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.17
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.85
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.86
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.00
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.71
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.37
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.17
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.99
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.48
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.78
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.12
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.56
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.15
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.32
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.57
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.33
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.50
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.61
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.69
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 214                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9636.27
 p-value of test no 215                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.70
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.31
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.22
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.80
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11682.17
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.97
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.36
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999928784
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.37
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999945125
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.66
 p-value of test no 245                :  3.6e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    7.47
 p-value of test no 247                :  2.2e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.55
 p-value of test no 248                :    0.9998    *****
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:30.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  105  AutoCor, d=1, r=27              0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88801291.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56467
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     346
 p-value of test no 37                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 40                 :    0.9951
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    7.16
 p-value of test no 44                 :  2.9e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.49
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.70
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.90
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.86
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.09
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.90
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.44
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.48
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.30
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.12
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.50
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.58
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.62
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.74
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4932.73
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908023
   j =  2                              :            45987
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908346
   j =  2                              :            45821
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 79                 :  7.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-4
 p-value of test no 109                :  3.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 4.81e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 111                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.010
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.17
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.53
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.45
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.81
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.93
 p-value of test no 124                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.30
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.99
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.36
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.13
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.57
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.79
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.63
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.13
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.03
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.93
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.08
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.06
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.67
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.39
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.48
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.47
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.22
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.73
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.40
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.59
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.55
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.22
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.36
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.81
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.87
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.01
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.64
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.74
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.33
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.51
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.70
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.78
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.44
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.17
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.82
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.15
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.91
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.62
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.02
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.88
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.41
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.89
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.19
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.00
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.63
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.12
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000084727
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.99
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999966959
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 235                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 237                :  7.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 238                :    0.9932
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:12.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         2.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89751563.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56468
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.63
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.84
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.46
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.55
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.13
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.36
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.23
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.25
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.32
 p-value of test no 61                 :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.12
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.83
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.34
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46107
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907790
   j =  2                              :            46099
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908377
   j =  2                              :            45807
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 102                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.93e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.00
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.38
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.44
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.53
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.05
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.50
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.93
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.88
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.24
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.34
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.02
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.61
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.99
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.39
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.81
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.37
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.63
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.04
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.41
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.79
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.51
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.93
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.63
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.41
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.92
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.90
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.51
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.07
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.90
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.13
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.00
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.22
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.57
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.35
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.70
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.21
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.94
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.63
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.11
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.78
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.84
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.12
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.61
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10236.08
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.08
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.75
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.05
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.66
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.08
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.78
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.42
 p-value of test no 231                :  7.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999900260
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.17
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000013687
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:20.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90767371.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56469
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 12                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5551
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     659
 p-value of test no 31                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.37
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.69
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.87
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.73
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.35
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.30
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.79
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.71
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.89
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.73
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.04
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.24
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.09
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.60
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.90
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908653
   j =  2                              :            45663
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908380
   j =  2                              :            45810
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.97
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.95
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.92
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.26
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.57
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.41
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.84
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.24
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.64
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
 p-value of test no 138                :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.57
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17717.17
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.52
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.01
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.29
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.98
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.14
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.75
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.61
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.86
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.99
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.32
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.89
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.95
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.39
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.57
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.14
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.46
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.66
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.94
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.85
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.23
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.72
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.71
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.49
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.07
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.58
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.91
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.48
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.50
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.68
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.00
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.65
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.92
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.61
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.21
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.27
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.06
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000072934
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.09
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999985208
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:38.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91750411.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56470
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9919
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.37
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.45
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.48
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.92
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.61
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.39
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.83
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.08
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.99
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.03
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.62
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.73
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.15
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908562
   j =  2                              :            45716
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46207
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870207
   j =  1                              :        399907591
   j =  2                              :            46197
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.45e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.13
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.32
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.23
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.64
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.19
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.20
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.47
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.70
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.38
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.05
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.99
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.77
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.49
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.12
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.47
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.55
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.18
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.96
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.70
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.09
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.62
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.76
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.28
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.38
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.57
 p-value of test no 162                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.46
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.95
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.83
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.50
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.05
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.51
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.14
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.18
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.22
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.84
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.45
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.65
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  259.56
 p-value of test no 175                :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.48
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.16
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.69
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.32
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.28
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10295.27
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.02
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.77
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.67
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.95
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.58
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.61
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.32
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.18
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000041731
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.03
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000061852
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:23.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92667915.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56471
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.22
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.43
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.29
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.85
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.11
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.42
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.45
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.98
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.37
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.33
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.82
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.51
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.90
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.90
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46342
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870342
   j =  1                              :        399907323
   j =  2                              :            46328
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.88e-4
 p-value of test no 109                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-5
 p-value of test no 110                :    0.9906
 
 Anderson-Darling statistic = A2       :    4.80
 p-value of test no 111                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.72
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.98
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.77
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.99
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.69
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.37
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.29
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.62
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17764.70
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.26
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.40
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.21
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.75
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.30
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.72
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.67
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.81
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.35
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.69
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.76
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.06
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.17
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.66
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.90
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.45
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.58
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.07
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.47
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.06
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.75
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.76
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.81
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.78
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.55
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.54
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.05
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.38
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.33
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.98
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.88
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.55
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.55
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.08
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.41
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.94
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.23
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.31
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.11
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.00
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.02
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999947858
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.99
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999980420
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:23.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93945867.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56472
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    3.64
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9936
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.07
 p-value of test no 41                 :  8.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.47
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.94
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.47
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.51
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.12
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.50
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.55
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.88
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.04
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.88
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.28
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 63                 :  1.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.62
 p-value of test no 64                 :  1.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   94.13
 p-value of test no 65                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.69
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.28
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.87
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908125
   j =  2                              :            45930
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907937
   j =  2                              :            46030
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 105                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.27
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.90
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.97
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.29
 p-value of test no 122                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.10
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.32
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.45
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.81
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.91
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.96
 p-value of test no 137                :  9.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.30
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.25
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.43
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.51
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.26
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.18
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.53
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.32
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.12
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.49
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.01
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.88
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.26
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.04
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.92
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.55
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.79
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.96
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.26
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.50
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.80
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.23
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.61
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.80
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5270.86
 p-value of test no 168                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  309.57
 p-value of test no 169                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.95
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.37
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.40
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.89
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.26
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.40
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.69
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.18
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 180                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.11
 p-value of test no 196                :  6.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 200                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.74
 p-value of test no 203                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.08
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10221.23
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10307.93
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.68
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 223                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5093.25
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4348.23
 p-value of test no 227                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.96
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.99
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.23
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.06
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999819329
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.51
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999887723
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:10.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  71  MatrixRank, L=5000              9.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94896139.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56473
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 4                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7634
 p-value of test no 21                 :  1.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.33
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.63
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.24
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.93
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.83
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.34
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.08
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.39
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.05
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.04
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.29
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.39
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.39
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908100
   j =  2                              :            45950
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908149
   j =  2                              :            45918
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.07
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.91
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.77
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.94
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.38
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.26
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.10
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.11
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.92
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.19
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.95
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.96
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.31
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.70
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.35
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.22
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.12
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.85
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.50
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.21
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.39
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.84
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.50
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.12
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.27
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.13
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.29
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.01
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.23
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.99
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.92
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.08
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.78
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.54
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.36
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.32
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.20
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.95
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.79
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.08
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.11
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.58
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.19
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.90
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.22
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.20
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.96
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.45
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999925928
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.45
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999858275
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:02.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        1.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95879179.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56474
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5604
 p-value of test no 13                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.99
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.30
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.63
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.65
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.22
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.43
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.62
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7261.18
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.26
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.27
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.26
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.34
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908440
   j =  2                              :            45771
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908325
   j =  2                              :            45833
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.84
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.43
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.91
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.58
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.50
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.42
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.26
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.25
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17287.99
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.09
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.18
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.85
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.62
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.19
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.30
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.70
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.27
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.96
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.95
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.31
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.33
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.50
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.43
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.28
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.07
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.19
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.19
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.64
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.95
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.20
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.94
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.29
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.14
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.84
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.73
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.95
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.97
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.16
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.88
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.38
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.49
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.85
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.13
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.73
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.92
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.91
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.06
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.53
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.87
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.78
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999932162
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.14
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000004549
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:29.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96894987.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56475
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4131
 p-value of test no 14                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    4.00
 p-value of test no 32                 :  8.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.21
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.13
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.03
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.74
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.19
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.56
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.05
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.23
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.81
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.97
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.81
 p-value of test no 65                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.93
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.70
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908368
   j =  2                              :            45813
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908524
   j =  2                              :            45735
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.57
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.04
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.14
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.39
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.65
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.82
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.93
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.35
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.52
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.50
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.47
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.78
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.36
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.57
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.45
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.32
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.58
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.80
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.25
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.71
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.05
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.22
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.26
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.23
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.79
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.26
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.64
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.06
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.44
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.65
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.35
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.58
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.86
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.10
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.30
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.97
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.85
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.47
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.51
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.76
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.64
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.79
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.62
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.49
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.06
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.10
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.22
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.38
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.91
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.81
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.22
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.03
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.66
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000033715
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.59
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999989288
 
 Normal statistic for number of bits   :  -0.085
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.057
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:21.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97910795.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56476
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.19
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 39                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.24
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.51
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.54
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.46
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.99
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.02
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.89
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.55
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.81
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.01
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.01
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.54
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.83
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5270.09
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907850
   j =  2                              :            46069
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908302
   j =  2                              :            45843
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.51
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.35
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.69
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.11
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   68.67
 p-value of test no 123                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.62
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.31
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.14
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.30
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.59
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.40
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.57
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.30
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.74
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.06
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.17
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.49
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.39
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.19
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.77
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.57
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   89.76
 p-value of test no 159                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.63
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.70
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.56
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.88
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.06
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.70
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.42
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.10
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.03
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.36
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.02
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.78
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.38
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.66
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.30
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.16
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.44
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    2.25
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.98
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.86
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.73
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.41
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9699.27
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5088.65
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.95
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.55
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.64
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.37
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11537.64
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.78
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999969836
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.58
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999978119
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:39.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98861067.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56477
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.40
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.29
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.05
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.01
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.55
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.21
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.81
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.37
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.36
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.24
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.10
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.40
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.42
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907942
   j =  2                              :            46023
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907895
   j =  2                              :            46051
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-4
 p-value of test no 110                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.76
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.81
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.41
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.80
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.33
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.20
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.54
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.08
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.53
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.90
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.23
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.42
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.25
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.87
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.95
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.37
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.42
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.45
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.51
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.82
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.73
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.94
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.94
 p-value of test no 162                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.59
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.25
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.78
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.72
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.10
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.25
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.17
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.22
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.08
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.89
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4784.77
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.79
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.51
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.11
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.90
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.71
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.49
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.72
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.52
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.03
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.23
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.16
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.35
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.39
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.51
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000031012
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.30
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999925322
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:07.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99811339.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56478
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.15
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.55
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.43
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.75
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.75
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.44
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.18
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.22
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.43
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.44
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.22
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.65
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.12
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.92
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908357
   j =  2                              :            45811
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907848
   j =  2                              :            46067
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.52
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.34
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.92
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.87
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.67
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.82
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.20
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.57
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.58
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.52
 p-value of test no 148                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.11
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.57
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.70
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.70
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.82
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.66
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.62
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.49
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.51
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.84
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.72
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.26
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.21
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.22
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.48
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.66
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.73
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.37
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.98
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.61
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.38
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.43
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.05
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.08
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.12
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.76
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.73
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.96
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.87
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.80
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.00
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.10
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.95
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.52
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.88
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.18
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.75
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999904541
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.92
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000039949
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:25.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100859915.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56479
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.73
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.62
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.70
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.44
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.12
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.80
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.46
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.75
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.85
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.14
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.97
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.03
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5237.58
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908025
   j =  2                              :            45986
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907737
   j =  2                              :            46127
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.45
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.29
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.85
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.38
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.60
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.75
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.00
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.58
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.96
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.49
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.73
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.49
 p-value of test no 146                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.80
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.05
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.00
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.83
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.39
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.43
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.29
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.81
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.86
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.68
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.56
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.66
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.37
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.40
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.06
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.02
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.06
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.82
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.06
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.07
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.46
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.06
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.62
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.30
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.03
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.64
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.31
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.07
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.21
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.76
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.64
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.66
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.70
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.16
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11606.68
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.41
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.75
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000055651
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.50
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000040243
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    3.24
 p-value of test no 239                :  6.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:25.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101679115.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56480
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1225
 p-value of test no 11                 : 1 -  6.7e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334345
   j =  1                              :        599997550
   j =  2                              :             1225
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.68
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.30
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.36
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.94
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.65
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.12
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.06
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.53
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7279.99
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.26
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.61
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.43
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5253.56
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907953
   j =  2                              :            46022
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908191
   j =  2                              :            45897
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
 p-value of test no 84                 :    0.9952
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.71
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.93
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.25
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.24
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.36
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.69
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.77
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.24
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.53
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.43
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.13
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.31
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.84
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.30
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.83
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.38
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.73
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.28
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.21
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.45
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.76
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.19
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.95
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.35
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.08
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.57
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.42
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.68
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.80
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.55
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.74
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.88
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.46
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.28
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.45
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.72
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.41
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.22
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.62
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.12
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.18
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.58
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.79
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.29
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.36
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.95
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999918182
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.79
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999933962
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    2.10
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:50.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  6.7e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82378766.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56481
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.43
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.15
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.20
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.37
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.25
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.26
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.90
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.41
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.55
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.31
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.54
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.62
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.78
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.56
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908367
   j =  2                              :            45812
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    4.44
 p-value of test no 102                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.67
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.49
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.27
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.18
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.18
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.65
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.31
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.37
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.28
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.31
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.81
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.76
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.98
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.13
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.72
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.50
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.90
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.68
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.01
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.19
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.85
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.16
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.26
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.58
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.46
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.85
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.69
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.89
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.64
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.14
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.10
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.14
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.31
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.81
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.98
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.95
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.51
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.31
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.71
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 195                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.21
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.82
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.18
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.71
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.11
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.05
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4293.73
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.33
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11544.88
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.00
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.79
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000046066
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.73
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000128407
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:10.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83656718.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56482
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5295
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9927
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.20
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.66
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.13
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.33
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.04
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.09
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.48
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.81
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.99
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6913.90
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.43
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.29
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.85
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.53
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.09
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908930
   j =  2                              :            45529
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46222
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870222
   j =  1                              :        399907565
   j =  2                              :            46204
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    6.79
 p-value of test no 85                 :  4.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.42
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.83
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.95
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.32
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.56
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.43
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.41
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.60
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.89
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.70
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.48
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 142                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17787.17
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.89
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.37
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.22
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.15
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.15
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.84
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.90
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.94
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.40
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.45
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.23
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.72
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.85
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.36
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.07
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.64
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.97
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.75
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.95
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.71
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.94
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.06
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.70
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.72
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.28
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.26
 p-value of test no 203                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 206                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  258.43
 p-value of test no 207                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.60
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.24
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.07
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.41
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.51
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.50
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.70
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.95
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.11
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000148726
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.50
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000010099
 
 Normal statistic for number of bits   :   0.080
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.24
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:36.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft AD, t = 16               4.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84541454.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56483
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 11                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.50
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.33
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.04
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.01
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.01
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.13
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.04
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.24
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.64
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.79
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.08
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.90
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.09
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.38
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.25
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908397
   j =  2                              :            45794
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907988
   j =  2                              :            46000
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 77                 :  9.8e-5    *****
 
 Anderson-Darling statistic = A2       :    8.42
 p-value of test no 78                 :  7.7e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.61
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.26
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.01
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.62
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.69
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.87
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.20
 p-value of test no 134                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.82
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17468.32
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.01
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.89
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.40
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.30
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.14
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.08
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.46
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.32
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.06
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.08
 p-value of test no 156                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.23
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.23
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.77
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.91
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.28
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.21
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.66
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.38
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.54
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.81
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.42
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.07
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.72
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.12
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.07
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.78
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.77
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.45
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.00
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 187                :  8.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.56
 p-value of test no 188                :    0.9948
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.88
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.86
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.95
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
 p-value of test no 213                :    0.9950
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9701.59
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.39
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.38
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.59
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.88
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.72
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.90
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.90
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999937907
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.61
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000007186
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    2.26
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:40.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft AD, t = 8                7.7e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85491726.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56484
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    3.71
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.32
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.40
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.23
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.17
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.51
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.77
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.77
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.03
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.97
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.94
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.26
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.67
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.90
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.13
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4841.54
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46182
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870182
   j =  1                              :        399907641
   j =  2                              :            46172
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908497
   j =  2                              :            45750
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.95
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.39
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.00
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.89
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.34
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.78
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.62
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.15
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.63
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17150.81
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.81
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.37
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.11
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.37
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.43
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.62
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.28
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.69
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.54
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.70
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.74
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.34
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.87
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.74
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.08
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.02
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.58
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.58
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.33
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.10
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.85
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.12
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.07
 p-value of test no 170                :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.70
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.44
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.03
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.00
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.04
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.87
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.87
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.08
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.88
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.72
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.74
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.58
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.20
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.85
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.08
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.59
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.91
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000123193
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.71
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000000259
 
 Normal statistic for number of bits   : 2.05e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    2.29
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:11.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86376466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56485
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.71
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.56
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.28
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.32
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.27
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.17
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.05
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7210.69
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.26
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.86
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.66
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.78
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908365
   j =  2                              :            45807
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45446
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869446
   j =  1                              :        399909111
   j =  2                              :            45440
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-4
 p-value of test no 100                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.95e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.60
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.76
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.09
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.94
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.16
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.81
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.34
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.40
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.76
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17267.17
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.11
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.16
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.99
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.72
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.19
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.19
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.08
 p-value of test no 152                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.67
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.28
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.03
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.32
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.17
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.12
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.48
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.36
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.85
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.78
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.50
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.99
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.66
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.53
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.26
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.25
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.88
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.27
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.96
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.53
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.84
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.18
 p-value of test no 184                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-4
 p-value of test no 190                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.23
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.76
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.35
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.53
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.42
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.77
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.76
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.40
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.74
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.36
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.54
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.97
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000070000
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.69
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999922799
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:29.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87326738.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56486
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1245
 p-value of test no 10                 :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334365
   j =  1                              :        599997510
   j =  2                              :             1245
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.53
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.41
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.54
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.21
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.85
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.70
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7243.35
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.71
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.75
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.41
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.11
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908851
   j =  2                              :            45567
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908639
   j =  2                              :            45676
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-5
 p-value of test no 113                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.06
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.66
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.97
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.14
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.61
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.47
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.68
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.44
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.08
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.98
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.75
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.83
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.87
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.18
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.50
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.26
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.53
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.28
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.97
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.11
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.38
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.13
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.52
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.63
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.24
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.92
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.24
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.39
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.99
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.78
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.33
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.37
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.42
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.74
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.21
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.55
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.79
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.40
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.68
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.80
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.62
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.25
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.64
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.35
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.46
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.41
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.62
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.08
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.78
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.42
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999909983
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.89
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999967913
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:56.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9994 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88473618.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56487
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7556
 p-value of test no 20                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.24
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.98
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.18
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.30
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.60
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.31
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.94
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.18
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.99
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
 p-value of test no 59                 :    0.9966
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.25
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.00
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.44
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.96
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.41
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907577
   j =  2                              :            46207
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907766
   j =  2                              :            46111
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.62
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.40
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.05
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.04
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.41
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.91
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.82
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.42
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17666.44
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.91
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.38
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.29
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.68
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.95
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.17
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.30
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.72
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.66
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.13
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.22
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.48
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.10
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.72
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.79
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.36
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.05
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.30
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.00
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.76
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.54
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.50
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.54
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.76
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.51
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.01
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.38
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.02
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.65
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.08
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.87e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.64
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.80
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.60
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.82
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.51
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.97
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.17
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000082561
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.69
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999967334
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:44.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89554962.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56488
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   22.93
 p-value of test no 46                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.25
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.27
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.43
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.88
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.83
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.14
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.76
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.40
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.03
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.63
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.37
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.33
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.91
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.17
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.05
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.90
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45316
 p-value of test no 70                 :    0.9958
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869316
   j =  1                              :        399909372
   j =  2                              :            45308
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 80                 :    0.9960
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.10
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.66
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.14
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.84
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.85
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.90
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.26
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.61
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.69
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.93
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.23
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.00
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.44
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.17
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.64
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.59
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.70
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.37
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.06
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.84
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.68
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.22
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.81
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.58
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.71
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.02
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.85
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.32
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.13
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.97
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.31
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.37
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.83
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.33
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.77
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.09
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.68
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.40
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.12
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.18
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.68
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.38
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.01
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.05
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.78
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.55
 p-value of test no 231                :    0.9908
 
 
 -----------------------------------------------
 Total number of bits:  8000008605
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.09
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000019489
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.013
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:57.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90472466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56489
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 5                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 10                 :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.09
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.95
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.08
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.09
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.59
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.73
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.02
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.32
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.11
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.19
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.77
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.60
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.08
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45764
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908477
   j =  2                              :            45754
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908493
   j =  2                              :            45746
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.75
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.94
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.18
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.15
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.96
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.78
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.73
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.32
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.33
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.63
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.08
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.28
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.13
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.86
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.05
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.88
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.49
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.99
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.30
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.54
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.97
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.36
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.97
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.59
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.38
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.01
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.59
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.72
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.77
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.54
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.46
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.20
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.81
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.60
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.71
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.84
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.64
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.14
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.18
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.26
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.88
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.25
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.82
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.28
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4682.80
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.90
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.73
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.27
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.57
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.19
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999942911
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.71
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000112615
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:24.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91586578.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56490
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.93
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.74
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.73
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.21
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.91
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.90
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.56
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.18
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.09
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.17
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.18
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.30
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.04
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.39
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.72
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.11
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.06
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908266
   j =  2                              :            45864
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908375
   j =  2                              :            45808
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.40
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.72
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.89
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.26
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.41
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.61
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.59
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.79
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.31
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.15
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.01
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.26
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.97
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.42
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.57
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.29
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.58
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.08
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.15
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.55
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.85
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.56
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.29
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.54
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.29
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.19
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.02
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.29
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4811.60
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.38
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.78
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.48
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.88
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.87
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.49
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.43
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.15
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.93
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.86
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.24
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 208                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10236.63
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.93
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.65
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.00
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3836.17
 p-value of test no 227                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.73
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.55
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.31
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.00
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999995417
 
 Normal statistic for number of bits   :  -0.036
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.37
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999979166
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:12.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  97  HammingIndep, L=300, r=0        0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92536850.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56491
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.46
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.10
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    3.72
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.30
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.93
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.60
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.87
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.39
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.82
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.78
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7268.52
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.07
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.67
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.71
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.27
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.76
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46327
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870327
   j =  1                              :        399907347
   j =  2                              :            46325
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.90
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.99
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.67
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.67
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.62
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.83
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.62
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 127                :  4.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 128                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.62
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.64
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.85
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17684.24
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.66
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.10
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.70
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.93
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.35
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.48
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.43
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.28
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.69
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.24
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.38
 p-value of test no 160                :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.08
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.89
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.62
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.75
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.06
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.63
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.51
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.77
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.29
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.84
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.09
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.59
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.50
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.46
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.36
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.67
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.87
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.31
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.88
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
 p-value of test no 219                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.56
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.55
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.59
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4266.58
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.50
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.89
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.81
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000017011
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.96
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999950132
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:29.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93519890.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56492
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.33
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.08
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.53
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.53
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.64
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.84
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.63
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.46
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.49
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.72
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.74
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.84
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.38
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4896.99
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46111
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870111
   j =  1                              :        399907780
   j =  2                              :            46107
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907989
   j =  2                              :            46001
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.69
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.15
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.19
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.83
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.20
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.02
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.93
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.44
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.69
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.09
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.20
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.10
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.90
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.80
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.67
 p-value of test no 149                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.01
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.89
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.26
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.45
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.40
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.85
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.05
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.77
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.46
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.22
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.83
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.92
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.07
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.18
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.56
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.44
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.07
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.06
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.00
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.44
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.67
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.14
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.34
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.13
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.72
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.76
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.63
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.92
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.01
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 221                :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5172.53
 p-value of test no 222                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.51
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.93
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.98
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.93
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.39
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.08
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000099301
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.92
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000177403
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:42.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94601234.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56493
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.21
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.47
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    3.71
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.84
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.76
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.83
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.84
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.83
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.06
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.07
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.64
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.43
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.81
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.23
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.51
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.26
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.02
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46099
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870099
   j =  1                              :        399907806
   j =  2                              :            46091
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908568
   j =  2                              :            45713
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 98                 :  2.6e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.38
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.06
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.83
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.20
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.60
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.11
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.55
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.36
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.89
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.32
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.28
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.57
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.44
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.80
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.08
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.92
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.94
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.47
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.33
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.81
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.50
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.81
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.28
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.71
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.60
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.91
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.59
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.27
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.22
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.33
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.82
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.26
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.25
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.91
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.69
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.28
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.05
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   25.64
 p-value of test no 198                :  1.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.56
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.30
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.35
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.15
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.20
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.32
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.85
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.13
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.82
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.62
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.19
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999923858
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.70
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999963674
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 1.02e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:47.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95682578.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56494
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 11                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 41                 :    0.9950
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.92
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.07
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.97
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.81
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.09
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.17
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.77
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.78
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.75
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.45
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.91
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.52
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907891
   j =  2                              :            46050
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908099
   j =  2                              :            45946
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.32
 p-value of test no 116                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.55
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.33
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.95
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.50
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.44
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.37
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.82
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.85
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.23
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.53
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.33
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.22
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.62
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.24
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.38
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.82
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.51
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.09
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.60
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.16
 p-value of test no 158                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.40
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.81
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.00
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.94
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.97
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.69
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.70
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.95
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.98
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.77
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.60
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.53
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.06
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.56
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.11
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.45
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.27
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.31
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.49
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.66
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.81
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.48
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.90
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.78
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.51
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.01
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.16
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.68
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999925166
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.15
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000055237
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:30.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96567314.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56495
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7524
 p-value of test no 19                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.25
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.10
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.47
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.94
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.07
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.80
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.29
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.09
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.07
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.13
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.81
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.37
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.57
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.56
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.36
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45517
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869517
   j =  1                              :        399908971
   j =  2                              :            45507
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.58
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.46
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.03
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.18
 p-value of test no 124                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.23
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.14
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.62
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.31
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.31
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.74
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.39
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.90
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.70
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.17
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.22
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.78
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.91
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.48
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.16
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.30
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.04
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.73
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.42
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.66
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.84
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.52
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.04
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.26
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.10
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.93
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.18
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.74
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.75
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.02
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.72
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.09
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.06
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.61
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.38
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.42
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.00
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.94
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.85
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.14
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.67
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.84
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.37
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000009280
 
 Normal statistic for number of bits   :   0.073
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.98
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000175516
 
 Normal statistic for number of bits   :    1.39
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:02.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97583122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56496
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.69
 p-value of test no 29                 :  4.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9929
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.00
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.16
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.49
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.94
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.98
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.64
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.91
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.79
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.56
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.15
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.53
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.33
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.00
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46242
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870242
   j =  1                              :        399907521
   j =  2                              :            46232
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908575
   j =  2                              :            45705
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-3
 p-value of test no 104                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.46
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.11
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.24
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.21
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.21
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.66
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.30
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.44
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.46
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.77
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 144                :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.30
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.91
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.05
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.61
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.76
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.72
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.18
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.58
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.25
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.06
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.67
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.44
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.18
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.27
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.30
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.07
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.05
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.72
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.73
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.77
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.38
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.52
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.34
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.42
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.39
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.06
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.50
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.98
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.97
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.03
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.21
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.85
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.31
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.24
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.26
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.91
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.46
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.19
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.40
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.86
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.28
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.87
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.92
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999992684
 
 Normal statistic for number of bits   :  -0.058
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.45
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000006829
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.72e-3
 p-value of test no 246                :    0.9962
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.58
 p-value of test no 248                :    0.9951
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:45.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98500626.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56497
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 11                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.54
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.80
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.14
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.59
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.81
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.34
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.14
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.48
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.69
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.51
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.12
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.59
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.31
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.34
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.62
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45510
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869510
   j =  1                              :        399908983
   j =  2                              :            45504
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908606
   j =  2                              :            45691
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 91                 :  2.5e-4    *****
 
 Anderson-Darling statistic = A2       :    9.98
 p-value of test no 92                 :  1.5e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.84
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.12
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.18
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.09
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.07
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.62
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.91
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17150.33
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.48
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.20
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.52
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.40
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.54
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.64
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.35
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.56
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.18
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.54
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.26
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.15
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.56
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.33
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.83
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.10
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.40
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.45
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.07
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.87
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.11
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.70
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.09
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.28
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.52
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.62
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.91
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.52
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.82
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.32
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.09
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.93
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.70
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.53
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.89
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.47
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.54
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.70
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.92
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.03
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999957161
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.22
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000018301
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:34.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft AD, t = 24               1.5e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99581970.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56498
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.62
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.49
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.81
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.81
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.20
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.28
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.23
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1583.06
 p-value of test no 56                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7181.98
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.81
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.17
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.57
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.30
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.51
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908367
   j =  2                              :            45812
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46181
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870181
   j =  1                              :        399907644
   j =  2                              :            46169
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 101                :    0.9966
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.73
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.13
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.89
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.62
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.85
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.23
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.30
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.66
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.83
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17775.45
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.75
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.19
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.28
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.49
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.89
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.85
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.88
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.61
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.53
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.30
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.36
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.44
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.01
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.24
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.75
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.58
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.37
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.97
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.53
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.11
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.95
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.49
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.17
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.23
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.82
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.39
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.90
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.11
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.87
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.73
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.50
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.10
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.53
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.23
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.26
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.77
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.19
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.98
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.22
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.29
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.99
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000001123
 
 Normal statistic for number of bits   : 8.88e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.53
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000063895
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 238                :    0.94
 
 Sample variance                       :    2.04
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:00.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100597778.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56499
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   24.01
 p-value of test no 47                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.24
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.14
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.32
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.80
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.87
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.40
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.31
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.02
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.39
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-3
 p-value of test no 59                 :    0.9974
 
 Anderson-Darling statistic = A2       :    5.35
 p-value of test no 60                 :  2.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.32
 p-value of test no 61                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.08
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.86
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.87
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4838.97
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907939
   j =  2                              :            46026
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908096
   j =  2                              :            45943
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.41
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.28
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.77
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.44
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.18
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.48
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.11
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.09
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.19
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.66
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.50
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.43
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.73
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.64
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.27
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.36
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.83
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.32
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.55
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.82
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.44
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.16
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.70
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.60
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.62
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.45
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.58
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.23
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.89
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.26
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.69
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.99
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.23
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.58
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.81
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.09
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.62
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.99
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.30
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.27
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.19
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.00
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.90
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.51
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.35
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.75
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.45
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.62
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.04
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999876650
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.56
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000002536
 
 Normal statistic for number of bits   :   0.020
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:22.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101613586.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56500
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.57
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.28
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.77
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.95
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.87
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.22
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.22
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.06
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.88
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.37
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.14
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.63
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.50
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.28
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.02
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.39
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907892
   j =  2                              :            46048
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907792
   j =  2                              :            46101
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.64
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.95
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.81
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.26
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.17
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.46
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.30
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.26
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.47
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.61
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.10
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.93
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.61
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.79
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.14
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.81
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.68
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.62
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.33
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.28
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.36
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.33
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.76
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.93
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.65
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.53
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.82
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.67
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.59
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.61
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.64
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.35
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.34
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.80
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.86
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.40
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.97
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.30
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.20
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.71
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.67
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.73
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.30
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.92
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4708.18
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.46
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.56
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.90
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.43
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.30
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.64
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000114547
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.88
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000170005
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:52.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82411535.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56501
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.67
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.94
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.08
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.20
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.81
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.97
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6885.96
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.70
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.43
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.99
 p-value of test no 67                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.91
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46159
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907685
   j =  2                              :            46153
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908035
   j =  2                              :            45978
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.64
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.21
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.87
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.93
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.69
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.81
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.08
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.31
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.05
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.79
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.18
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.54
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.31
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.03
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.84
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.37
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.66
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.56
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.65
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.83
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.28
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.41
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.29
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.23
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.54
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.30
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.68
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.38
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.91
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.45
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.93
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.69
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.19
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.05
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.86
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.06
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.50
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.38
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.31
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.92
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.44
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.38
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.27
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.56
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.91
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.61
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.59
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.73
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11488.28
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12215.20
 p-value of test no 230                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.06
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999930413
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999898160
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:12.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83197980.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56502
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.97
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.66
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.46
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.08
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.60
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.34
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.24
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.90
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.05
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7166.71
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.00
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 63                 :    0.9929
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.30
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.61
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.96
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908071
   j =  2                              :            45957
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907754
   j =  2                              :            46117
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.55
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.17
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.95
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.44
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.27
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.60
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.71
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.52
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.91
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17150.29
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.44
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.40
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.33
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.70
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.16
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.17
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.17
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.19
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.11
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.53
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.98
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.60
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.00
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.72
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.75
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.94
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.60
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.44
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.03
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.98
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.52
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.39
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.87
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.05
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.00
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.26
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.54
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.43
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.06
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.07
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :-7.02e-17
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.94
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.11
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.27
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.17
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.64
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9748.65
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.55
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.20
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.80
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.05
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.61
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.93
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.92
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999994217
 
 Normal statistic for number of bits   :  -0.046
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.02
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000039769
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.036
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:32.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84574236.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56503
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 12                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    3.86
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.67
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.53
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.80
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.17
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.50
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.10
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.04
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.58
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.51
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.60
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.29
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.37
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.36
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.88
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908657
   j =  2                              :            45664
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.87
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.43
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.84
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.20
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.22
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.16
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.04
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.39
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.25
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.79
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.20
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.87
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.59
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.10
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.41
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.98
 p-value of test no 157                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.37
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.05
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.63
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.76
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.24
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.85
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.48
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.73
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.12
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.17
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.02
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.00
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.30
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.92
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.99
 p-value of test no 172                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.02
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.97
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.32
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.13
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.04
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.44
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.45
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.95
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.83
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.84
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5061.79
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.07
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.42
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.11
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.10
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.13
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.29
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999904328
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.49
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000027472
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 240                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.42
 p-value of test no 243                :  7.7e-3
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 245                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.13
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:44.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85524508.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56504
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.73
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.29
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.13
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.19
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.27
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.35
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.61
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.70
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.27
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.66
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.88
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.96
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.46
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.19
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907909
   j =  2                              :            46044
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908188
   j =  2                              :            45900
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 78                 :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.73
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.68
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.86
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.9916
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.61
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.93
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.43
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.92
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.11
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.74
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.32
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.52
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.89
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.69
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.25
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.84
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.49
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.63
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.23
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   39.66
 p-value of test no 160                :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.50
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.87
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.92
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.40
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.87
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.50
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.44
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.34
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.76
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.60
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.13
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.93
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.27
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.12
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.22
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.68
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.94
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.95
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.44
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.35
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.88
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 223                :  2.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 225                :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4650.72
 p-value of test no 226                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.93
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.81
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.73
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.18
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999972353
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.83
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000035161
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 242                :    0.9994    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:24.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86474780.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56505
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 6                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    3.66
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.13
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.73
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.98
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.75
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.41
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.77
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.98
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.09
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.44
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.27
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.60
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.30
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.59
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.26
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908083
   j =  2                              :            45951
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907856
   j =  2                              :            46066
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 86                 :  4.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 88                 :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9958
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 91                 :    0.9904
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.00
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.23
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.21
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.78
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.25
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.56
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.04
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.17
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.29
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.61
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.02
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17187.64
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.16
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.46
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.32
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.10
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.53
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.68
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.37
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.80
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.36
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.02
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.03
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.73
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.27
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.45
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.58
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.52
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.37
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.35
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.13
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.02
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.41
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.97
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.20
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.42
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.00
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.27
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.25
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.46
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.37
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.80
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.75
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.92
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.49
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10247.26
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 213                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.24
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.41
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.06
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.57
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.68
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.52
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.24
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.23
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000028039
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.45
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999905324
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:00.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87392284.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56506
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 10                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7110
 p-value of test no 21                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    3.73
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.9911
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.42
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.66
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.44
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.11
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.77
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.24
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1341.27
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.32
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.32
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 62                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 64                 :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.35
 p-value of test no 65                 :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.47
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.76
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.73
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908591
   j =  2                              :            45697
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908301
   j =  2                              :            45842
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.40
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.89
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.12
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.32
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.73
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.99
 p-value of test no 129                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.72
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.13
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.28
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17343.52
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.18
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.27
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.60
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.43
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.80
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.56
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.05
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.26
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.62
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.93
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.43
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.24
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.43
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.81
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.38
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.59
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.14
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.40
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.00
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.17
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.71
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.26
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.91
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.53
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.33
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.07
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.65
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.85
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.79
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.91
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.50
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.23
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.45
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.63
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.31
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.06
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.21
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.44
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.86
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000173296
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.88
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999954290
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9905
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.023
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:28.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88440860.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56507
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 5                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.13
 p-value of test no 44                 :    0.9995    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.37
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.17
 p-value of test no 48                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.95
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.07
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.89
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.36
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.69
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.90
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.62
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.24
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.54
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.76
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.29
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908747
   j =  2                              :            45622
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908118
   j =  2                              :            45938
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.09
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.48
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.58
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.00
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.14
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.39
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.90
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.76
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17677.26
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.96
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.38
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.37
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.13
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.38
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.13
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.80
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.26
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.76
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.36
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.08
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.85
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.81
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.26
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.33
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.94
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.35
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.86
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.39
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.31
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.30
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.91
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.69
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.44
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.55
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.94
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.99
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.30
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.23
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.09
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.58
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.79
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.37
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.20
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5124.53
 p-value of test no 226                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.39
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.24
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.78
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.70
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.72
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000102724
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.67
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999948266
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:52.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89391132.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56508
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.42
 p-value of test no 40                 :  2.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.93
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.96
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.80
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.06
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.82
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.96
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.04
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.77
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.66
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7313.82
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.87
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.55
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.65
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.23
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907604
   j =  2                              :            46195
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 94                 :  3.0e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.04
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.79
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.57
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.34
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.80
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.26
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.30
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.23
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.87
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.67
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.75
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.69
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.70
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.71
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.64
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.48
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.61
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.82
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.48
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.59
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.86
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.30
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.91
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.62
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.93
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.15
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.54
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.77
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.34
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.66
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.15
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.90
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.13
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.82
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.67
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.85
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.31
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.75
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.88e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.18
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.97
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.01
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.48
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.34e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.16
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.07
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.03
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.64
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.76
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.76
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.61
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999992330
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.90
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999944663
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 246                :    0.9908
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:54.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90603548.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56509
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9919
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.49
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.90
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.69
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.97
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.02
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.25
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.14
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.57
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.92
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.11
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.12
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907910
   j =  2                              :            46039
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908349
   j =  2                              :            45824
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.06
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.33
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.52
 p-value of test no 122                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.36
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.47
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.76
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.61
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.31
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17459.89
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.23
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.74
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.17
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.73
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.89
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.85
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.38
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.68
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.11
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.61
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.66
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.40
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.59
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.63
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.80
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.02
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.02
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.19
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.92
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.35
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.96
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.26
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.79
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.30
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.57
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.64
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.35
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.05
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.17
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.28
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.80
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.43
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.53
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.75
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.62
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.17
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.29
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.46
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999986834
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.32
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000196387
 
 Normal statistic for number of bits   :    1.55
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.063
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.072
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:38.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91619356.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56510
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    4.44
 p-value of test no 27                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9945
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.82
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.57
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.74
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.24
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.65
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.18
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  179.78
 p-value of test no 54                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.27
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.05
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7152.80
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.92
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
 p-value of test no 63                 :    0.9970
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.93
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.73
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.46
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907692
   j =  2                              :            46151
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.43
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.93
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.01
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.32
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.00
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.03
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.57
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.27
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.37
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.85
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.88
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.47
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.15
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.05
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.93
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.85
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.12
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.69
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.65
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.89
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.38
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.35
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.67
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.27
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.14
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.76
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.03
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.07
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.03
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.24
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.27
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.99
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.40
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.19
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.59
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.07
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.50
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.97
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10275.71
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.96
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.04
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.98
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.13
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.27
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.55
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.14
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999928334
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.86
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999986585
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:02.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92602396.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56511
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.63
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.44
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.52
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.30
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.99
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.31
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1336.62
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.70
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.24
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.26
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.01
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.80
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.94
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907720
   j =  2                              :            46137
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907797
   j =  2                              :            46094
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    5.32
 p-value of test no 99                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.73
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.87
 p-value of test no 120                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.88
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.10
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.83
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.60
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.12
 p-value of test no 133                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.06
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.79
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.12
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.93
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.99
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.39
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.23
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.25
 p-value of test no 153                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.01
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.15
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.53
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.14
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.24
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.44
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.99
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.67
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.34
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.55
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.80
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.35
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.61
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.42
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.94
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.95
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.18
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.32
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.45
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.39
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.50
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.65
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.67
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.53
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.06
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.27
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.17
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.35
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.18
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.52
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.01
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.33
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.06
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.00
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000043345
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.01
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999951032
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:40.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94011420.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56512
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.30
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.31
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.88
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.29
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.23
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.17
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.67
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7254.50
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.27
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.63
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.78
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.48
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.63
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907964
   j =  2                              :            46015
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908094
   j =  2                              :            45947
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 83                 :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.79
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.02
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.18
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.97
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.18
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.86
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.92
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.52
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.39
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17203.45
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.04
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.25
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.92
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.68
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.05
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.23
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.34
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.91
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.85
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.34
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.38
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.70
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.93
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.41
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.82
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.33
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.14
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.64
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.84
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.91
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.24
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.82
 p-value of test no 170                :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.47
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.61
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.34
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.91
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.55
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.18
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.78
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.83
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.21
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.30
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10282.02
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.07
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.31
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.36
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.12
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.61
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.39
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12070.50
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.91
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000059299
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.84
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999953834
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    2.27
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:43.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94961692.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56513
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.74
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.34
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.68
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.20
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.83
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.71
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1329.78
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.91
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.68
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.33
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.80
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.38
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.58
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907742
   j =  2                              :            46126
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908252
   j =  2                              :            45871
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.75
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.98
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.69
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.51
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.25
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.24
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.28
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.73
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17440.76
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.02
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.16
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.40
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.01
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.88
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.28
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.62
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.83
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.83
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.27
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.11
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.23
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.00
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.05
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.55
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.72
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.56
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.62
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.64
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.00
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.62
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.31
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.95
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.45
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.92
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.73
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.11
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.78
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.51
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.92
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.97
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.32
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.73
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.68
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.20
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.16
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999900560
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.42
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000197800
 
 Normal statistic for number of bits   :    1.56
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95944732.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56514
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    3.63
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 40                 :    0.9973
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.92
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.29
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.29
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.68
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.64
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.61
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.89
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.51
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1556.57
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.92
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.15
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.70
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.70
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.80
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.97
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908582
   j =  2                              :            45706
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908555
   j =  2                              :            45721
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 76                 :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 115                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.03
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.25
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.42
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.07
 p-value of test no 124                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.05
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.57
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.22
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.04
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.07
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.00
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.06
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.03
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.89
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.59
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.22
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.10
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.52
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.12
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.94
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.68
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.38
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.10
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.66
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.92
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.75
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.12
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.16
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.46
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.49
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.15
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.53
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.44
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.69
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.26
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.22
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.34
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.76
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.68
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.85
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.73
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9735.65
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9751.38
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.54
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.53
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.77
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.07
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.76
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.35
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.37
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999927350
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.11
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999979166
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.64
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 248                :    0.51
 
 Sample variance                       :    2.20
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:18.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96993308.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56515
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9911
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.75
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.92
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.39
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.78
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.22
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.05
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.93
 p-value of test no 55                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.80
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.60
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.63
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.85
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.45
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.91
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5282.02
 p-value of test no 68                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907926
   j =  2                              :            46031
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46337
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870337
   j =  1                              :        399907327
   j =  2                              :            46335
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 97                 :  5.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.92
 p-value of test no 99                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.33e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.45
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.14
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.28
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.91
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.25
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.87
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 130                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 131                :  1.6e-4    *****
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 132                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.57
 p-value of test no 133                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.43
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 139                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.58
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17578.25
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.65
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.29
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.46
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.62
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.87
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.07
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.15
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.85
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.53
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.22
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.33
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.13
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.05
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.50
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.13
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.28
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.96
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.20
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.82
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.18
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.02
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.80
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.06
 p-value of test no 171                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.03
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.44
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.45
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.48
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.53
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.63
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.21
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.83
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.62
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.23
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.78
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.20
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.10
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4268.20
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.39
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.34
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.32
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.12
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999925628
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.36
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999957281
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:01.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98009116.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56516
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.14
 p-value of test no 34                 :  2.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.14
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.75
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.89
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.98
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.72
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.83
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7250.94
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.11
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.06
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.03
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.21
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.70
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45435
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869435
   j =  1                              :        399909133
   j =  2                              :            45429
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908015
   j =  2                              :            45985
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.61
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.84
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.82
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.35
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.05
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.69
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.73
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.01
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.25
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.16
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.83
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.55
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.66
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.30
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.79
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.74
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.87
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.37
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.82
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.06
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.66
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.31
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.66
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.23
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.33
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.38
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.26
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.88
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.16
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.26
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.95
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.53
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.36
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.91
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.32
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.77
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.74
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.25
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.45
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.79
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.23
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.49
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.20
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.41
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.04
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.43
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11320.35
 p-value of test no 229                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.18
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.54
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999895394
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.04
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999844118
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:14.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  99  HammingIndep, L=1200, r=0       0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99024924.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56517
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 4                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 9                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    3.10
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.75
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.94
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.52
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.22
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.33
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.18
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7156.78
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.55
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.97
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.61
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.17
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46145
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907715
   j =  2                              :            46135
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907894
   j =  2                              :            46047
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 106                :  9.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.33
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.40
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.36
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.38
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.44
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.29
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
 p-value of test no 126                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.61
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.87
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.50
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.51
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.85
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.62
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.54
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.30
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.08
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.69
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.85
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.76
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.42
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.70
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.08
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.03
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.22
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.71
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.31
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.29
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.98
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.47
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.23
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.72
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.20
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.93
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.91
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.67
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.73
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.20
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.57
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.10
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.18
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.92
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.69
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.42
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.11
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.07
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9703.55
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.69
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.29
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.68
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.68
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.31
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.63
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.64
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999989333
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.33
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000021808
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:03.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100106268.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56518
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    3.60
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.40
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.90
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.22
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.48
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.55
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.66
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.73
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.56
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.06
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.46
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.37
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.76
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.61
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908208
   j =  2                              :            45890
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908116
   j =  2                              :            45936
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.70
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.67
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.08
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.94
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.86
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.72
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.39
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.29
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.34
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.86
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.78
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.33
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.75
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.71
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.51
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.48
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.61
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.59
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.84
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.36
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.24
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.32
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.51
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.84
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.40
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.26
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.29
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.34
 p-value of test no 166                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.69
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.66
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.10
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.77
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.32
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.63
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.86
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.16
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.23
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.54
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.08
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.95
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.88
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.39
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.37
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.21
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.48
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.68
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.58
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.12
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.11
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.29
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.86
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000025672
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.34
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000037138
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    2.02
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:42.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101154844.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56519
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.29
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.80
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.31
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.39
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.20
 p-value of test no 53                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.99
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.83
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.73
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.56
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.84
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.80
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.52
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.04
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.60
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908041
   j =  2                              :            45978
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45450
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909104
   j =  2                              :            45442
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.19
 p-value of test no 119                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.10
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.83
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.68
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.28
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.35
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.25
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.97
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.38
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.51
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.73
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.78
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.17
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.90
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.74
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.52
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.90
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.64
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.27
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.37
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.06
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   95.41
 p-value of test no 159                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.75
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.37
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.95
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.37
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.80
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.62
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.31
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.45
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.56
 p-value of test no 169                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.86
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.21
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.63
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.45
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.28
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.32
 p-value of test no 175                :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.75
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.82
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.26
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.96
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.06
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 221                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.32
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.04
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.47
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.70
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.87
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.46
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.59
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000062527
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.29
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999913655
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.88
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:30.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102170652.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56520
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1233
 p-value of test no 11                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334353
   j =  1                              :        599997534
   j =  2                              :             1233
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    3.75
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.67
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.58
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.93
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.48
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.80
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.14
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.55
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.92
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.95
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.41
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.44
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.31
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45593
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869593
   j =  1                              :        399908819
   j =  2                              :            45583
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908408
   j =  2                              :            45787
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.42
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.02
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.39
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.52
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.94
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.60
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 138                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.46
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17092.92
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.27
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.91
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.01
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.40
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.59
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.13
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.40
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.16
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.09
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.11
 p-value of test no 156                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.80
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.76
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.37
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.80
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.77
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.11
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.33
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.07
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.47
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.86
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.78
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.86
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.05
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.46
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.43
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.66
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.40
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.14
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.15
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 181                :    0.9939
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.41
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.88
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.03
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.10
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.27
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.31
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.93
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.13
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.30
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.52
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.69
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.66
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999995726
 
 Normal statistic for number of bits   :  -0.034
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.91
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000114724
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9942
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:03.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82444304.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56521
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.52
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.64
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.72
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.67
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.70
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.64
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.16
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.57
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.33
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.52
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.88
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.78
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.26
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.99
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.24
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45539
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908924
   j =  2                              :            45535
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908812
   j =  2                              :            45588
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.72
 p-value of test no 116                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.54
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.24
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.03
 p-value of test no 123                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.10
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.01
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.36
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.12
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.12
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.82
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.56
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.57
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.20
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.64
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.95
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.01
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.28
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.91
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.34
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.52
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.61
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.82
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.80
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.64
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.18
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.90
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.95
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.36
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.10
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.46
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.20
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.74
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.85
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.01
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.85
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.66
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.98
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.25
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.14
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.55
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.00
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.59
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.96
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.55
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.82
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.07
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.34
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999906629
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.79
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000086770
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 253                :    0.07
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:24.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83722256.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56522
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.66
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.65
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.49
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.93
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.46
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.49
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.96
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7213.45
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.13
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.72
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.82
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.93
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908273
   j =  2                              :            45859
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46219
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907567
   j =  2                              :            46209
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.99
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.84
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.48
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.52
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.11
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.83
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.85
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.98
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.25
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.95
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.10
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.46
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.85
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.71
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.18
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.46
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.75
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.18
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.01
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.40
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.71
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.41
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.21
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.38
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.91
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.15
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.20
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.43
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.01
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.40
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.13
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.12
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.20
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.16
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.06
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.47
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.68
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.03
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.08
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.60
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.90
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
 p-value of test no 204                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.93
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.30
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.16
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.89
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.74
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.31
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3841.88
 p-value of test no 228                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.97
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.61
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.17
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000001306
 
 Normal statistic for number of bits   :   0.010
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.10
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000069082
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.88e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:48.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  98  HammingIndep, L=300, r=26       0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84312089.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56523
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7074
 p-value of test no 20                 :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9933
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.98
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.52
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.30
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.25
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.04
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.46
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.45
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.51
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.29
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   51.65
 p-value of test no 61                 :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.80
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.31
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.06
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.87
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908311
   j =  2                              :            45840
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46183
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907637
   j =  2                              :            46177
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.27
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.60
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.00
 p-value of test no 123                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.19
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.29
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.29
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.45
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 135                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.68
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.19
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.41
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.32
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.07
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.59
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.07
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.57
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.32
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.67
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.75
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.01
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.23
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.04
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.11
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.97
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.01
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.18
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.25
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.77
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.64
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.05
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.70
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.01
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.22
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.22
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.20
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.44
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.32
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.52
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.51
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.99
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.99
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.32
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 214                :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10385.39
 p-value of test no 215                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.24
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 223                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4652.95
 p-value of test no 226                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.47
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.41
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.48
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.57
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.06
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000072718
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.29
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999795437
 
 Normal statistic for number of bits   :   -1.62
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 237                :  3.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.00
 p-value of test no 238                :  1.4e-3
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:32.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85098521.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56524
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 10                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.81
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.52
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.27
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.98
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.32
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.52
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.95
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.55
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.40
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 59                 :    0.9925
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.37
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.65
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.80
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.00
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.07
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908337
   j =  2                              :            45827
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908149
   j =  2                              :            45924
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.05
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.16
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.14
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.83
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.32
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.55
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.06
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.86
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.78
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.48
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.17
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.54
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.58
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.21
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.62
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.84
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.64
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.77
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.58
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.83
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.70
 p-value of test no 158                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.26
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.89
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.66
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.15
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.35
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.68
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.25
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.43
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.94
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.32
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.97
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.95
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.57
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.77
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.83
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.20
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.92
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.60
 p-value of test no 176                :  6.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.91
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.27
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.82
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.53
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10296.81
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.74
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.47
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.33
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.82
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.80
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.32
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.37
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.58
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999886505
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.97
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000073372
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    2.50
 p-value of test no 244                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.015
 p-value of test no 248                :    0.49
 
 Sample variance                       :    2.13
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86147097.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56525
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    4.16
 p-value of test no 44                 :  7.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.31
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.56
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.23
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.03
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.77
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.81
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7311.58
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.43
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.41
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.13
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.52
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908100
   j =  2                              :            45947
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908596
   j =  2                              :            45693
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  8.4e-3
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 94                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 95                 :  9.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  9.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 101                :  5.5e-4    *****
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 102                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.85
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.71
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.29
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.25
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.14
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.30
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 127                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.02
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.84
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.04
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17531.38
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.58
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.04
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.75
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.45
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.06
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.06
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.93
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.30
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.02
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.61
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.79
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.52
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.54
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.83
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.26
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.07
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.87
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.83
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.95
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.11
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.82
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.42
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.72
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.09
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.67
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.48
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.50
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.12
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.46
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.92
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.73
 p-value of test no 176                :    0.9972
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 201                :    0.9904
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.51
 p-value of test no 203                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.45
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.04
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.49
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.90
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.23
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.39
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3908.89
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.16
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.83
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.03
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000020014
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999918263
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:01.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87130137.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56526
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7583
 p-value of test no 18                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.92
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.80
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.57
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.75
 p-value of test no 52                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.89
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.54
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.31
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.87
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.45
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.97
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.42
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.84
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.15
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908637
   j =  2                              :            45677
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908464
   j =  2                              :            45753
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.12
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.72
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.68
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.22
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.70
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.05
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 128                :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.45
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.68
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.60
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.80
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.80
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.22
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.74
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.13
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.32
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.95
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.66
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.92
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.92
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.41
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.93
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.76
 p-value of test no 157                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.54
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.85
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.63
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.29
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.01
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.26
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.13
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.93
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.16
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.76
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.31
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.50
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.00
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.13
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.94
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.71
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.73
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.72
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.10
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.33
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.07
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.73
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.83
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.55
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.65
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.85
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.64
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.48
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.88
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.99
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11465.90
 p-value of test no 230                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.00
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999996908
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.42
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000061126
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:57.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88244249.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56527
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    6.73
 p-value of test no 39                 :  4.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9918
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.45
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.06
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.94
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.70
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.48
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.01
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.34
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.80
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1537.03
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.41
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.06
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.44
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.42
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.66
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.52
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907825
   j =  2                              :            46080
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908514
   j =  2                              :            45740
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.89
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.18
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.42
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.18
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.60
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.35
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.23
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.50
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.97
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.92
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 139                :    0.9926
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 140                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   87.86
 p-value of test no 141                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.13
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.21
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.59
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.13
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.58
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.68
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.97
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.21
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.77
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.80
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.76
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.40
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.45
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.29
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.18
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.33
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.70
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.29
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.13
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.09
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.48
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.77
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.47
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4820.70
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  301.34
 p-value of test no 174                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.59
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.00
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.31
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.65
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.19
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.76
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9780.74
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.60
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.00
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.92
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.39
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.49
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.52
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.60
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.63
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000082147
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.43
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000005317
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 241                :    0.9938
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.13
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:38.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2S, t = 9         4.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89489420.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56528
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.38
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.43
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.33
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.39
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.13
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.60
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.19
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.02
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6945.68
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.11
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.30
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.38
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.76
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908565
   j =  2                              :            45710
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46260
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870260
   j =  1                              :        399907482
   j =  2                              :            46256
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.60
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.94
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.74
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.90
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.51
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.49
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.99
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.55
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17440.53
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.64
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.54
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.24
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.05
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.26
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.29
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.31
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.58
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.85
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.76
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.57
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.42
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.86
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.80
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.73
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.88
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.85
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.05
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.44
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.45
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.81
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.16
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.19
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.48
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.10
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.68
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.06
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.64
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.18
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.48
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.81
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-3
 p-value of test no 205                :    0.9983
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.35
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.33
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.40
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4718.41
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.20
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.12
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.54
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.24
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.12
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.06
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000015931
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.17
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999985826
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.062
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:01.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90374156.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56529
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     659
 p-value of test no 31                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.70
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.17
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.16
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.06
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.27
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.95
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.07
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.06
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7153.67
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.83
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.24
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.23
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.98
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.37
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908483
   j =  2                              :            45757
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908074
   j =  2                              :            45960
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 85                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.69
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.26
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.29
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.06
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.20
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.67
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.09
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.52
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.32
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.46
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.09
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.22
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.14
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.96
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.69
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.48
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.65
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.69
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.14
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.45
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.46
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.91
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.69
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.77
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.55
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.48
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.29
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.81
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.65
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.32
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.69
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4726.85
 p-value of test no 168                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.36
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.74
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.79
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.61
 p-value of test no 172                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.15
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.19
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.43
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.15
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.87
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.18
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.78
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.92
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.88
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9821.58
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.76
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.37
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.49
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.26
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.78
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11550.06
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.06
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000092302
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.21
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999931013
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.062
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:00.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91291660.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56530
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7125
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.23
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   97.95
 p-value of test no 51                 :  2.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.06
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.78
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.67
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6913.91
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.27
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.30
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.62
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5197.73
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908674
   j =  2                              :            45654
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908406
   j =  2                              :            45791
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 95                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9962
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.30
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.43
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.95
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.46
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.13
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.02
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.95
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.41
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.99
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.50
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.04
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.26
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.55
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.29
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.45
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.94
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.68
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.58
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.77
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.36
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.13
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.03
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.94
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.90
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.05
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.87
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.64
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.48
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.21
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.96
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.16
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.11
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.25
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.59
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.39
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.09
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.40
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.15
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.80
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.84
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 212                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10308.67
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.63
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.20
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.65
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.78
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11542.52
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.96
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.74
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999811055
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.80
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999853916
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    2.04
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:21.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         2.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92307468.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56531
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7582
 p-value of test no 21                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.28
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.90
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.48
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.89
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.93
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1526.39
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.77
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.27
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.59
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.93
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.82
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.30
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46207
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870207
   j =  1                              :        399907594
   j =  2                              :            46191
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907970
   j =  2                              :            46009
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.43
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.55
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.57
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.23
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.98
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.79
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.81
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.96
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.74
 p-value of test no 135                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.06
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17400.08
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.62
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.38
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.41
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.92
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.38
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.50
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.18
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.76
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.69
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.40
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.58
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.21
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.10
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.45
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.56
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.70
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.12
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.57
 p-value of test no 164                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.68
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.17
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.00
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.61
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.71
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.03
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.56
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.74
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.84
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.14
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.06
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 201                :    0.9955
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.84
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.16
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.49
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.56
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.27
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.95
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.73
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.82
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.85
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.20
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.68
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000024796
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.63
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999973388
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:50.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93323276.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56532
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997165
   j =  2                              :             1416
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.30
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.30
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.64
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.91
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.48
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.47
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  372.48
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.28
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.42
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.61
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.54
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.28
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.85
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908005
   j =  2                              :            45993
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908732
   j =  2                              :            45625
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.41
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.35
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.67
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.86
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.93
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.62
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.46
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.84
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.14
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.83
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.44
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.05
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.50
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.61
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.33
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.14
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.60
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.32
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.14
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.46
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.90
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.67
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.61
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.00
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.64
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.22
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.04
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.96
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.39
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.70
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.82
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.50
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.73
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.50
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.25
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.79
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.56
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.90
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.28
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.92
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.96
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.21
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 181                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.68
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.32
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.15
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10254.60
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.43
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.46
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.31
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.89
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.66
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.93
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.94
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.68
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000115048
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.81
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000104620
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:15.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94339084.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56533
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.22
 p-value of test no 22                 :  6.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    4.38
 p-value of test no 45                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.68
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.47
 p-value of test no 48                 :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.02
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.28
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.07
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.82
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.83
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.40
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.28
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.41
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.12
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.91
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.42
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.59
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46183
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907639
   j =  2                              :            46173
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45539
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908922
   j =  2                              :            45539
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-3
 p-value of test no 77                 :    0.9984
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-3
 p-value of test no 83                 :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.27
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.29
 p-value of test no 120                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.11
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.72
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.58
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.03
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.56
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.60
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.98
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17142.99
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.23
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.45
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.13
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.95
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.15
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.24
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.38
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.51
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.72
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.21
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.51
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.17
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.72
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.40
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.51
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.43
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.16
 p-value of test no 167                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.34
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.97
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.05
 p-value of test no 170                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.70
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.96
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.64
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.09
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.13
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.22
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.29
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.00
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.14
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.39
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.92
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.22
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.83
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.98
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.63
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.12
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.04
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.54
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000054757
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.31
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999947558
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:46.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95322124.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56534
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 7                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997235
   j =  2                              :             1381
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 10                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.06
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    7.25
 p-value of test no 29                 :  2.7e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.19
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.16
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.74
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.53
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.81
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.58
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.50
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.80
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.26
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.63
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.15
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.57
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.93
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.35
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.72
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907915
   j =  2                              :            46035
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907729
   j =  2                              :            46128
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.68
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.23
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.94
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.95
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.48
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.10
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.97
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.82
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.73
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.09
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17273.17
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.70
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.29
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.91
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.27
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.36
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.92
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.54
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.83
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.06
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.61
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.12
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.45
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.07
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.12
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.76
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.15
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.29
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.88
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.40
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.64
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.80
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.66
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.75
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.18
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.06
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.33
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.05
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.13
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.11
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.88
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.57
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.91
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.77
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.88
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.12
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12033.64
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.14
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.61
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000056344
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.61
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000142894
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    2.36
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:37.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP, t = 5           2.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96272396.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56535
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.93
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.36
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.42
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.56
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.43
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.84
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.66
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.57
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.37
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.00
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.43
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.22
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.36
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.67
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.42
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.65
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908226
   j =  2                              :            45878
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907623
   j =  2                              :            46187
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.73
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.47
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.99
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.72
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.23
 p-value of test no 125                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 127                :    0.9918
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.28
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.79
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.20
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17181.89
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.39
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.43
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.85
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.17
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.55
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.26
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.37
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.70
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.16
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.33
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.42
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.23
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.00
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.81
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.46
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.56
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.15
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.01
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.50
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.68
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.27
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.64
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.48
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.71
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.19
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.34
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.94
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.55
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.95
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.99
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.78
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.18
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.22
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4720.95
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.13
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.10
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.12
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.31
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.46
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.23
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999984149
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.47
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999957764
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.00e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.21
 p-value of test no 244                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:38.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97288204.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56536
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4193
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7100
 p-value of test no 19                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.23
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.39
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.94
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.41
 p-value of test no 49                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.07
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.91
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.46
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.15
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.68
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.41
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7085.37
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.16
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.26
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.80
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.40
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908207
   j =  2                              :            45895
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 100                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 117                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.00
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.80
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.88
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.36
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.81
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.81
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.97
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.17
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.09
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17780.75
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.21
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.54
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.03
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.83
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.83
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.14
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.01
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.90
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.41
 p-value of test no 154                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.50
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.94
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.21
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.39
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.46
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.19
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.48
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.43
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.71
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.26
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.73
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.47
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.29
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.15
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.61
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.91
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5314.06
 p-value of test no 173                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.61
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.77
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.76
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.08
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.72
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.27
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.46
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9705.41
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.76
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 224                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.28
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.68
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.05
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.98
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.90
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.72
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999951656
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   88.76
 p-value of test no 233                :  2.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999985394
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:19.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98304012.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56537
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9951
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.00
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.66
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.22
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.03
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.24
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.46
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.26
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.08
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.73
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.33
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.14
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.66
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.57
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908095
   j =  2                              :            45942
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907961
   j =  2                              :            46012
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.39
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.56
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.03
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.86
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.96
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.69
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.32
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.63
 p-value of test no 129                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.83
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.36
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.93
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.19
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.41
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.12
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.61
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.88
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.32
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.36
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.10
 p-value of test no 153                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.58
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.96
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.80
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.01
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.39
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.94
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.44
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.50
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.66
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.46
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.25
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.87
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.91
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.60
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.00
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.65
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.20
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.31
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.14
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.96
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.21
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.92
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.76
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.30
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.05
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.23
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.30
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.60
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4322.84
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.19
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.37
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.55
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999983015
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.46
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999842942
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    2.43
 p-value of test no 244                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:04.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99319820.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56538
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 3                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.73
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    5.13
 p-value of test no 33                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.08
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.42
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.83
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.89
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.69
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.44
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.60
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.14
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.30
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.45
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.66
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.08
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908828
   j =  2                              :            45577
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908156
   j =  2                              :            45919
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 115                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.29
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.86
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.91
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.56
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.30
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.04
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.78
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.52
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.23
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17236.10
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.84
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.75
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.67
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.64
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.34
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.90
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.82
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.99
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.35
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.50
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.52
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.63
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.20
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.13
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.53
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.26
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.32
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.34
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.34
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.31
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.64
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.52
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.58
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.67
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.61
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.86
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.80
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.59
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.09
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.20
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.46
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.08
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.74
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.42
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.01
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.39
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.09
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.21
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.05
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.75
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.42
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.08
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999916658
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.41
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000028735
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:10.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100335628.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56539
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7083
 p-value of test no 20                 :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.47
 p-value of test no 28                 :  5.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.30
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.37
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.76
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.49
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.95
 p-value of test no 50                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.85
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.17
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.18
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.27
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7154.48
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.69
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.40
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.16
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.49
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908123
   j =  2                              :            45934
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908098
   j =  2                              :            45945
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.00
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.98
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.31
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.29
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.07
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.58
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.34
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.01
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.08
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.66
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17262.12
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.76
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.10
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.62
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.67
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.33
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.87
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.20
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.66
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.19
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.70
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.76
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.73
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.18
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.14
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.84
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.40
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.15
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.64
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.33
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.92
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.83
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.54
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.30
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.80
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.47
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.11
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.81
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.30
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 206                :    0.9960
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.86
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.06
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.32
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.17
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.14
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.87
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.06
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.73
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.24
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.09
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000036199
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.58
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000043357
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -1.80e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:13.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101416972.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56540
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5328
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    3.79
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.58
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.65
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.60
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.61
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.95
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.19
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.19
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.48
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.46
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.46
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.22
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.69
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5204.36
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908179
   j =  2                              :            45900
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45635
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869635
   j =  1                              :        399908733
   j =  2                              :            45629
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.02
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.58
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.84
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.22
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.85
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.52
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.17
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.18
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 139                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 140                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.99
 p-value of test no 141                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17534.86
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.65
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.11
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.64
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.82
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.24
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.69
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.93
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.99
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.62
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.40
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.25
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.55
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.84
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.62
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.51
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.58
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.01
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.25
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.20
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.46
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.52
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.35
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.03
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.36
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.61
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.63
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.67
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.99
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.36
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.85
 p-value of test no 178                :  8.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.22
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.10
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.89
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.20
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.62
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.40
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.91
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.77
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.41
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12055.85
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.18
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.07
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999955586
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.23
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999936854
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:45.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82477073.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56541
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.90
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.58
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.38
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.19
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.23
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.63
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.13
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.07
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.99
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7227.41
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.23
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.39
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.03
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.27
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.34
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908699
   j =  2                              :            45649
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908520
   j =  2                              :            45731
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.40
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.65
 p-value of test no 120                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.20
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.43
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.70
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.83
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17301.55
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.04
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.72
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.92
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.61
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.03
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.65
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.70
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.08
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.04
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.33
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.28
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.12
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.95
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.99
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.59
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.94
 p-value of test no 162                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.08
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.73
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.34
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.39
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.23
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.50
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.25
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.37
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.83
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.68
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.63
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.16
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.10
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.94
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.82
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.14
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.53
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.13
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.72
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.78
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.29
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.03
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.93
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.71
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12156.01
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11366.99
 p-value of test no 230                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.27
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999961250
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.24
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999937655
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.92
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:35.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83918865.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56542
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9974
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    3.12
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.32
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.13
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.92
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.22
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.23
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.83
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.16
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.60
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.83
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.25
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.13
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.81
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.80
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.25
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908293
   j =  2                              :            45849
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45495
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869495
   j =  1                              :        399909018
   j =  2                              :            45479
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 117                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.26
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.14
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.30
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.03
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.75
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.00
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.18
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.32
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.67
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.68
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.49
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.49
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.26
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.05
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.50
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.26
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.01
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.53
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.69
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.15
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.38
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.06
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.69
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.91
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.70
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.29
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.56
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.07
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.51
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.39
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.58
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.81
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.86
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.00
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.44
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.18
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.71
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.13
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.63
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.17
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.87
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.82
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.61
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.89
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.35
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12100.23
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.22
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.78
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000006523
 
 Normal statistic for number of bits   :   0.052
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.62
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000087469
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.89
 
 Sample variance                       :    2.12
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:03.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84869137.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56543
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.58
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.89
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.40
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.30
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.04
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.21
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.35
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.21
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.11
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.11
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.90
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.68
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.45
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.94
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908154
   j =  2                              :            45917
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908073
   j =  2                              :            45959
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.10
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.53
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.78
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.21
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.39
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.67
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.53
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.49
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9958
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.83
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.62
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.03
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.02
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.53
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.37
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.66
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.12
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.73
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.73
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.47
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.79
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.17
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.90
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.27
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.13
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.22
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.69
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.72
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.10
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.09
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.26
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.09
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.09
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.50
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.74
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.51
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.08
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.17
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  259.28
 p-value of test no 203                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.59
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.79
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.95
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.52
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.07
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.84
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.65
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.10
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.86
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.33
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999900212
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.45
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999962507
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:07.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85884945.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56544
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.22
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.66
 p-value of test no 52                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.92
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.62
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.26
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.50
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.28
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.16
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.25
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4879.69
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907784
   j =  2                              :            46105
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908723
   j =  2                              :            45637
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-5
 p-value of test no 113                :    0.9958
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.74
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.06
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.16
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.22
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.89
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.19
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.38
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.38
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.97
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17224.95
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.45
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.68
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.13
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.43
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.42
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.86
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.78
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.03
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.84
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.55
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.66
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.82
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.96
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.84
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.99
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.73
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.03
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.89
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.02
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.60
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.98
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.66
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.55
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.82
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.70
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.66
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.80
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   36.89
 p-value of test no 178                :  2.3e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.85
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.25
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.69
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10258.72
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.55
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 220                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 221                :  8.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5126.18
 p-value of test no 222                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.42
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.34
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.07
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.01
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.34
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.21
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999923099
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.06
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000053599
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.86
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:00.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  81  LinearComp, r = 0               2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86802449.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56545
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 6                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9956
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.54
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.22
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.63
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.24
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.46
 p-value of test no 53                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.30
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.20
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.78
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7282.74
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.42
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.00
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.26
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.45
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908211
   j =  2                              :            45884
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908313
   j =  2                              :            45839
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.88
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.04
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.34
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.42
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.54
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.11
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.40
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.32
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.67
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.23
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.10
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.29
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.02
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.86
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.89
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.64
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.63
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.89
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.72
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.44
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.26
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.94
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.81
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.06
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.73
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.38
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.37
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.58
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.10
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.66
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.55
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.08
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.78
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.99
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.15
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.81
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.66
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.88
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.18
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.70
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.28
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.85
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.03
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.48
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.62
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.36
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.79
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.59
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.77
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.76
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.82
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.11
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000167029
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.31
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999995258
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.089
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    2.18
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 251                :    0.9939
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.54
 p-value of test no 253                :    0.9945
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:31.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87818257.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56546
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4173
 p-value of test no 16                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.72
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.58
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.64
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.25
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.45
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.96
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1521.25
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.22
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.01
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.04
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.59
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.39
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.78
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908733
   j =  2                              :            45623
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908143
   j =  2                              :            45924
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 78                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.03
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.29
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.13
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.15
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.62
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.12
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.82
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.90
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.53
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.59
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.83
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.51
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.58
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.49
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.27
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.23
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.28
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.61
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.99
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.85
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.34
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.77
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.56
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.90
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.72
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.56
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.80
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.33
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.84
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.96
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.38
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.87
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.04
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.81
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.11
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.91
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.11
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.25
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
 p-value of test no 213                :    0.9985
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9695.32
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.67
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.20
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.34
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3926.99
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.24
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.41
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999939806
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.06
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000032926
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.92
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:42.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88997905.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56547
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.77
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.42
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.46
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.18
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.68
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.10
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.39
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.61
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.02
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.64
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.87
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.73
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.02
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.78
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.79
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.91
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45299
 p-value of test no 70                 :    0.9967
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869299
   j =  1                              :        399909410
   j =  2                              :            45283
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46331
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870331
   j =  1                              :        399907341
   j =  2                              :            46325
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.11
 p-value of test no 120                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.24
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.88
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.90
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.55
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.26
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.34
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.96
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.13
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.16
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.83
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.28
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.99
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.44
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.46
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.33
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.77
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.14
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.09
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.33
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.29
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  420.24
 p-value of test no 163                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.23
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.77
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.21
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.81
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.94
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.85
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.81
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.32
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.23
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5218.63
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.65
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.12
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.65
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.68
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.34
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.60
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.75
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.91
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.30
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.40
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.41
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.58
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.22
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.70
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999930902
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.64
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000065203
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:11.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90013713.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56548
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1228
 p-value of test no 8                  : 1 -  9.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334348
   j =  1                              :        599997544
   j =  2                              :             1228
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4135
 p-value of test no 14                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.18
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.85
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.30
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.55
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.69
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.32
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.11
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.43
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.14
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.11
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.92
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.37
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 62                 :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.32
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.03
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5193.02
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907948
   j =  2                              :            46026
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907844
   j =  2                              :            46072
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.68
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.85
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.66
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.13
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.82
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.09
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.68
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.24
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.95
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.85
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.47
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.53
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.55
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.51
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.42
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.40
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.24
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.05
 p-value of test no 156                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.16
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.83
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.68
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.50
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.71
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.43
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.87
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.31
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.00
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.64
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.42
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5199.82
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.77
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.58
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.46
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.97
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.01
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.01
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.68
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.44
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.45
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.72
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.42
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9784.78
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.43
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.78
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.83
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.09
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.95
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.21
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.06
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.38
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000084496
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.61
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000017701
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    2.53
 p-value of test no 239                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 247                :  9.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 248                :    0.02
 
 Sample variance                       :    2.26
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.94
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:33.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7           1 -  9.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90996753.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56549
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.44
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.40
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.59
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.77
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.57
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.29
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.51
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.64
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.70
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.94
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.23
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.70
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.89
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908593
   j =  2                              :            45696
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908415
   j =  2                              :            45791
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.89
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.60
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.57
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.83
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.40
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.17
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.07
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.73
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.29
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.43
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.76
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.08
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.83
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.57
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.16
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.38
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.04
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.66
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.25
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.93
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.21
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.54
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.72
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.26
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.21
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.09
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.76
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.33
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.65
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.07
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.79
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.34
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.01
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.35
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.88
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.81
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.16
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.55
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.47
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.52
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.04
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.04
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.14
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.62
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.93
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-4
 p-value of test no 223                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 224                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    6.36
 p-value of test no 225                :  7.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5263.50
 p-value of test no 226                :  1.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.50
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3852.35
 p-value of test no 228                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.70
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.36
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.26
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000030709
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.01
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000007012
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:28.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  96  HammingIndep, L=30, r=27        1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91947025.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56550
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7055
 p-value of test no 18                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.01
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.89
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.22
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.63
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.76
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.46
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.95
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.96
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.31
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.48
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.88
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907865
   j =  2                              :            46063
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908448
   j =  2                              :            45773
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.01
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.40
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.70
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.69
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.29
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.65
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.50
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.57
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.86
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.39
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.82
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.62
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.30
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.12
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.23
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.65
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.88
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.00
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.42
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.56
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.71
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.24
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.63
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.17
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.01
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.19
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.43
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.25
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.65
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.34
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.99
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.15
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.36
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.98
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.51
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.48
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.78
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-4
 p-value of test no 213                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9782.88
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.40
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.50
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.79
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.60
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.15
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.16
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.53
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999971006
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.83
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999834716
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 252                :    0.9975
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:57.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92897297.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56551
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.48
 p-value of test no 34                 :  5.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.79
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.35
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.23
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.36
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.81
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.85
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.13
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.15
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6827.20
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.65
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.41
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.77
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.80
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.88
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907750
   j =  2                              :            46119
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907698
   j =  2                              :            46148
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.35
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.50
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.77
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.33
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.50
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.56
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.47
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.05
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 143                :    0.9921
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16980.38
 p-value of test no 145                :    0.9924
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.99
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.23
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.39
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.71
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.43
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.29
 p-value of test no 154                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.16
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.60
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.62
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.26
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.55
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.61
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.87
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.01
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.30
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.56
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.41
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.65
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.26
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.15
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.06
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.38
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.25
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.53
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.91
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.34
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.73
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.46
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.58
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.76
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.96
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.26
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.55
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.18
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.17
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.05
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.51
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.36
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.68
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.17
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.88
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000028369
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000071041
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:43.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93847569.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56552
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 6                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9912
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.66
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.41
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.56
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.12
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.22
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.93
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.01
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.99
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6736.38
 p-value of test no 57                 :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.47
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.24
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.15
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.41
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908480
   j =  2                              :            45754
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908121
   j =  2                              :            45938
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 4.12e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.49
 p-value of test no 115                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.30
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.03
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.66
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.45
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.08
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.03
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.11
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.02
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.56
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17295.58
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.32
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.82
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.93
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.97
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.11
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.95
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.13
 p-value of test no 152                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.47
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.06
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.99
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.80
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.25
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.50
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.45
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.41
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.38
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.40
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.77
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.60
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.66
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.19
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.51
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.58
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.70
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.34
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.14
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.02
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.03
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 185                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.32
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.78
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.20
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.58
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.52
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.64
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.05
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.59
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.30
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.06
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.72
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000126685
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.17
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999941690
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:38.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94797841.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56553
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.04
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.82
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.01
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.36
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.33
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.96
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.88
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.24
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.26
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.51
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.92
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.18
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.20
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.91
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.70
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907961
   j =  2                              :            46015
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908269
   j =  2                              :            45861
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 88                 :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9962
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-4
 p-value of test no 112                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.43
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.90
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.25
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.46
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.62
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.36
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.14
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.79
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.77
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.94
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.23
 p-value of test no 146                :    0.9900
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.55
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.50
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.75
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.41
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.04
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.18
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.33
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.40
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.35
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.42
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.00
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.34
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.96
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.47
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.07
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.61
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.08
 p-value of test no 166                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.94
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.63
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.50
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.31
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.30
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.93
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.63
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.48
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.95
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.76
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 180                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 181                :  3.2e-5    *****
 
 Anderson-Darling statistic = A2       :    8.31
 p-value of test no 182                :  9.1e-5    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.74
 p-value of test no 183                :  9.1e-5    *****
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.23
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.35
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.48
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.69
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.32
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 219                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4691.66
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.90
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.81
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3909.91
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.15
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12104.83
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.21
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999934916
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.25
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000114691
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:40.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  82  LempelZiv, r = 0                9.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95846419.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56554
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.28
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.99
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.15
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.88
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.10
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.56
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  377.79
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.59
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.96
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.11
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.48
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.15
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.40
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.78
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908662
   j =  2                              :            45663
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.45
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.25
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.86
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.69
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.08
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.33
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.64
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.26
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.61
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.82
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.57
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.65
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.89
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   56.64
 p-value of test no 148                :  3.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.37
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.95
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.06
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.35
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.47
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.44
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.04
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.69
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.92
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.92
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.16
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.43
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.06
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.20
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.67
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.11
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.59
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.29
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.70
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.41
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.06
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.65
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.13
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.74
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.96
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.37
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.69
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.56
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.75
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.15
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.36
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.58
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.41
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.59
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.69
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.87
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11568.92
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.84
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999761261
 
 Normal statistic for number of bits   :   -1.89
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.80
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000028786
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 241                :    0.9903
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.63
 p-value of test no 243                :    0.9957
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:21.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       3.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96862227.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56555
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.19
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.39
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.78
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.96
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.70
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.82
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.96
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.14
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.72
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.53
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 63                 :    0.9939
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.00
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.43
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.85
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45455
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869455
   j =  1                              :        399909093
   j =  2                              :            45449
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908415
   j =  2                              :            45785
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
 p-value of test no 97                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.08
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.89
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.63
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.37
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.99
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.98
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.19
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.10
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.23
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.35
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.72
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.99
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.27
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.93
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.57
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.19
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.36
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.15
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.05
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.58
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  602.05
 p-value of test no 158                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.75
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.28
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.03
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.36
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.96
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.10
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.55
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.36
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.41
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.02
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.72
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.15
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.56
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.97
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.22
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.04
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.77
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.96
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.84
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.02
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.15
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.42
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4674.74
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.68
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.44
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.86
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.12
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.34
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.29
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000096817
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.64
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999994004
 
 Normal statistic for number of bits   :  -0.047
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:32.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97812499.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56556
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.29
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.62
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.55
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.08
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.99
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.03
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.71
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  187.83
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.46
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.25
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.41
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.29
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.72
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.24
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.84
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907930
   j =  2                              :            46032
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907958
   j =  2                              :            46018
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.48
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.92
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.07
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.83
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.65
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
 p-value of test no 130                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.30
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.18
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.43
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.16
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.35
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.94
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.13
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.78
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.58
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.84
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.04
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.29
 p-value of test no 154                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.16
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.70
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.36
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.44
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.78
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.56
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.22
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.43
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.90
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.26
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.00
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.74
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.38
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.23
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.14
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.87
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.54
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.26
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.98
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.12
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.80
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.88
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.31
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.66
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.90
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.04
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.63
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.73
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.72
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.01
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.86
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999958904
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.91
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000058126
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.064
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.026
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:04.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98795539.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56557
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.57
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.50
 p-value of test no 40                 :  1.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.36
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.28
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.46
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.26
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.25
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.48
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.78
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.11
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.34
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.74
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.76
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.76
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.10
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.08
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.77
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46418
 p-value of test no 70                 :  6.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870418
   j =  1                              :        399907167
   j =  2                              :            46412
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908123
   j =  2                              :            45937
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.55
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.98
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.22
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.15
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.93
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.75
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.73
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.61
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.07
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.58
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17409.77
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.94
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.38
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.48
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.24
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.73
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.17
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.98
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.21
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.82
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.01
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.44
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.99
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.75
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.74
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.68
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.58
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.18
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.46
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.76
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.27
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.78
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.30
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.09
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.74
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.88
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.24
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.03
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.92
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.93
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.25
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.34
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.56
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.58
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.88
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.29
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.62
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.14
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.71
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.14
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999868478
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.95
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000027763
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:15.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99647507.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56558
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 3                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    3.88
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.50
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.88
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.12
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.03
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.64
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.35
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.61
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.52
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.04
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.90
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.37
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.25
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.61
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4981.23
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908378
   j =  2                              :            45805
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907575
   j =  2                              :            46211
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.48
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.31
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.51
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.84
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.22
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.80
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.38
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.53
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.29
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.17
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.35
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.83
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.22
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.85
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.44
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.66
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.89
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.32
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.31
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.39
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.22
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.53
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.62
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.38
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.69
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.10
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.66
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.86
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.92
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.22
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.39
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.92
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.60
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.46
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.83
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.58
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.83
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.30
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.17
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.00
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.92
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.21
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.75
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.54
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.45
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.67
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.65
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.85
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.17
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.68
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.77
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.87
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000122158
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.32
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999946856
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.73
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:02.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100630547.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56559
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.40
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.10
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.82
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.54
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.89
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.99
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.31
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.62
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.68
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.83
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.12
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.08
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.67
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908350
   j =  2                              :            45822
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907890
   j =  2                              :            46046
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 85                 :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.65
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.86
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.87
 p-value of test no 121                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.28
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.07
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.07
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.65
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.32
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.55
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.83
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.08
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.96
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.45
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.12
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.14
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.74
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.73
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.50
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.49
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.99
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.14
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.66
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.09
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.25
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.09
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.52
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.66
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.87
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.18
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.57
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.58
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.37
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.16
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.78
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.76
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.09
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.29
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.68
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.27
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.61
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.29
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.66
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 201                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 202                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  256.36
 p-value of test no 203                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.05
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.92
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.94
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.48
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.71
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.37
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.99
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.49
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.75
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000208132
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.48
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999956603
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:13.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101810195.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56560
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 3                  :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1217
 p-value of test no 8                  : 1 -  2.6e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334337
   j =  1                              :        599997566
   j =  2                              :             1217
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.82
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.88
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.47
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.07
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  292.56
 p-value of test no 54                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.49
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.57
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.64
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.74
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.02
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.94
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.07
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.07
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908067
   j =  2                              :            45959
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908546
   j =  2                              :            45718
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.55
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.14
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.93
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.66
 p-value of test no 122                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.40
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.66
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.73
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.80
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.94
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.50
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.80
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.52
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.34
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.02
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.21
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.72
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.26
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.07
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.39
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.30
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.09
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.27
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.59
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.86
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.52
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.60
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.95
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.45
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.08
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.13
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.88
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.34
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.33
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.64
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.54
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.65
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.38
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.94
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.04
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.62
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 190                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.27
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.11
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.65
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.09
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.37
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.26e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.06
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.82
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.89
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.94
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.24
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12038.74
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.08
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999905105
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.09
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999943223
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:09.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            7.8e-4
   8  CollisionOver, t = 7           1 -  2.6e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82509842.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56561
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7585
 p-value of test no 20                 :  9.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    4.44
 p-value of test no 36                 :  5.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     345
 p-value of test no 37                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.30
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.50
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.44
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.51
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.07
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.02
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  507.63
 p-value of test no 55                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.11
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6821.70
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.85
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.04
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.27
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.86
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.50
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908275
   j =  2                              :            45855
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908822
   j =  2                              :            45580
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 103                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.70
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.86
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.56
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.26
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.02
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.83
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.20
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.30
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 143                :    0.9948
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16952.08
 p-value of test no 145                :    0.9951
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.69
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.58
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.32
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.66
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.63
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.59
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.40
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.44
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.31
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.42
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.62
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.11
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.17
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.83
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.23
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.40
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.27
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.46
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.59
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.44
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.81
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  305.16
 p-value of test no 167                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.19
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.10
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.23
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.48
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.55
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.69
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.03
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.24
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.12
 p-value of test no 178                :  5.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.27
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    4.08
 p-value of test no 189                :  2.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.46
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.79
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.00
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.06
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.47
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.95
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.47
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.01
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.48
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.09
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.24
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.14
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999986711
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.18
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000059353
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:55.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        9.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83427337.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56562
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.89
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.01
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.03
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.25
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.68
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.48
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.75
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6863.78
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.71
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.59
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.60
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.58
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907755
   j =  2                              :            46118
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908576
   j =  2                              :            45706
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.82
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.62
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.16
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.87
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.37
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.13
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.37
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.17
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.95
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.96
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.17
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17132.78
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.30
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.16
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.08
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.45
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.91
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.13
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.38
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.42
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.63
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.95
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.42
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.60
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.66
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.11
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.84
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.60
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.34
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.67
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.64
 p-value of test no 166                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.19
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.50
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.11
 p-value of test no 169                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.46
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.04
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.83
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.84
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.25
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.86
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-4
 p-value of test no 190                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.08
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.91
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.92
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 213                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10221.10
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.38
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.49
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.56
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.42
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.91
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.92
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.69
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000027292
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.76
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000026020
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:44.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83984393.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56563
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    4.04
 p-value of test no 26                 :  8.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    6.20
 p-value of test no 38                 :  8.0e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.57
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.78
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.34
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.91
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.23
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.84
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.87
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.04
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.59
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.49
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.03
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.03
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.22
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.18
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908060
   j =  2                              :            45967
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908066
   j =  2                              :            45958
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.010
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.12
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.56
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.87
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.58
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.70
 p-value of test no 123                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.61
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.27
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.39
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.94
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 138                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  177.72
 p-value of test no 141                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17293.67
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.14
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.12
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.40
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.65
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.22
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.54
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.34
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.90
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.32
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.96
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.41
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.60
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.93
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.43
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.14
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.84
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.70
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.41
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.10
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.00
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.05
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.96
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.67
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.68
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.92
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.74
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.55
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.77
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.21
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.54
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 181                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 192                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.33
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.84
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.14
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.00
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.84
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.90
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.66
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.12
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.83
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.89
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.00
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999954035
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.49
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999976559
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:09.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          8.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85262345.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56564
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4527
 p-value of test no 17                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.62
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.06
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.64
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.20
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.95
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.13
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.07
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.07
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.24
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.42
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.10
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.24
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.27
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.42
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907743
   j =  2                              :            46121
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907942
   j =  2                              :            46017
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.42
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.34
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.15
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.79
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.97
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.30
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.35
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.55
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17128.27
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.16
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.06
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.80
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.25
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.15
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.58
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.59
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.04
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.66
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.74
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.70
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.99
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.53
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.13
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.09
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.56
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.77
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.64
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.45
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.46
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.21
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.70
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.68
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.34
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.30
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.73
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.70
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.43
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.58
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.84
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.71
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.60
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.41
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.82
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.17
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.60
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.03
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.60
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.98
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.08
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.12
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.25
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.07
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000010591
 
 Normal statistic for number of bits   :   0.084
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.51
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999925322
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:58.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86179849.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56565
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    3.13
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.42
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.43
 p-value of test no 48                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.77
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.67
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.91
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.82
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.14
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.94
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.37
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.35
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.64
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.48
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.79
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908328
   j =  2                              :            45833
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907742
   j =  2                              :            46123
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.29
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.91
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.21
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.46
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.72
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.95
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.20
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.46
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.77
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.24
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17241.99
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.80
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.22
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.87
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.02
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.18
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.99
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.13
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.80
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.20
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.12
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.25
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.67
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.75
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.84
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.76
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.14
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.64
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.87
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.48
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.66
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.16
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.13
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.62
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.61
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.10
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.61
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.89
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.61
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.31
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.68
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.56
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.31
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.25
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.36
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.51
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.13
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.62
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4355.66
 p-value of test no 228                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11500.51
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.84
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.45
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000001522
 
 Normal statistic for number of bits   :   0.012
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.33
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000065482
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:35.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87162889.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56566
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.19
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.58
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.23
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.54
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.23
 p-value of test no 52                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.96
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.74
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.18
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.52
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.02
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.93
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.86
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.66
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5256.97
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46202
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870202
   j =  1                              :        399907603
   j =  2                              :            46188
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45562
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869562
   j =  1                              :        399908878
   j =  2                              :            45558
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.90
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.02
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.26
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.57
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.15
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.79
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.51
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.36
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.29
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.84
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.13
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.61
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.67
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.50
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.20
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.14
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.86
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.48
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.02
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.58
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.81
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.14
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.54
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.49
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.54
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.99
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.74
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.39
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.22
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.18
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.96
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.23
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.41
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.77
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.68
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.24
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.04
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.10
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.13
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.41
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.06
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.41
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.34
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.03
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.84
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.48
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.58
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.05
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.11
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12059.19
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.44
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000017848
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.15
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999781172
 
 Normal statistic for number of bits   :   -1.73
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:09.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88080393.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56567
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.67
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 41                 :    0.9963
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.60
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.73
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.94
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  178.21
 p-value of test no 54                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.41
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.70
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.41
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.97
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   33.62
 p-value of test no 65                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.35
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.78
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.44
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46161
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870161
   j =  1                              :        399907680
   j =  2                              :            46157
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907865
   j =  2                              :            46063
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.23
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.03
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.36
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.87
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.33
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.35
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.55
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.48
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.06
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.93
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.39
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.59
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.30
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.12
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.31
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.52
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.13
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.42
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.43
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.22
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.20
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.41
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.50
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.96
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.40
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.17
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.70
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.21
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.99
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.07
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.72
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.03
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.29
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.14
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.66
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.04
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.48
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.99
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.83
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.93
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.07
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 223                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 225                :  9.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.43
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.55
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4316.55
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.14
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.05
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.76
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999871790
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.88
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000029596
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:16.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89096201.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56568
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.72
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.30
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.94
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.75
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.62
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.81
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.49
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.71
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.52
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.23
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.63
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.08
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.38
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.74
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4878.02
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908036
   j =  2                              :            45976
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908137
   j =  2                              :            45927
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.52e-4
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.97
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.19
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.80
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.61
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.76
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.69
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.88
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.55
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.44
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.15
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.39
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.51
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.19
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.85
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.26
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.72
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.51
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.57
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.34
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.96
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.34
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.45
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.45
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.26
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.04
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.13
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.56
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.84
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.23
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.43
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.08
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.54
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.84
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.47
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.99
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.98
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.38
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.47
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.62
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.46
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.77
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.70
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.55
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.48
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.04
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.54
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.73
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.31
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.03
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.06
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.42
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000040534
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.01
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000132124
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:08.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90079241.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56569
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1246
 p-value of test no 9                  :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334366
   j =  1                              :        599997508
   j =  2                              :             1246
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 10                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9951
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.18
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.83
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.22
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.06
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.52
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.51
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.41
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.96
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.75
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.51
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.78
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.18
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.62
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.44
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.30
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908114
   j =  2                              :            45937
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.82
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.18
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.19
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.78
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.81
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.42
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.29
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.69
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.84
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.36
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17152.63
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.09
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.63
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.86
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.15
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.72
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.86
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.42
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.29
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.80
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.39
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.63
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.43
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.94
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.66
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.63
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.48
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.40
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.79
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.93
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.89
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.19
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.99
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.03
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.30
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.31
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.39
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.12
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.26
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.25
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.99
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.45
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.50
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.17
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.56
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.19
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.10
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.15
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.69
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.90
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.95
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.44
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12183.94
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11579.52
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.40
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000096091
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.39
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999860756
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:42.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9994 
  10  CollisionOver, t = 14           5.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91095049.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56570
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.21
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.42
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.41
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.01
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.78
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.46
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   86.60
 p-value of test no 52                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.67
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.12
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.69
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.76
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.06
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.94
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.56
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.80
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5146.29
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908451
   j =  2                              :            45773
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907982
   j =  2                              :            46006
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.89
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.80
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.18
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.50
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.35
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.90
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.82
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 126                :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 128                :  8.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.80
 p-value of test no 129                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.30
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.38
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.36
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.01
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.56
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.87
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.17
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.07
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.42
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.51
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.39
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.91
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.98
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.76
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.89
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.62
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.75
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.54
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.22
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.88
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.52
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.82
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.15
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.90
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.66
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.00
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.17
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.85
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.65
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.34
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.33
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.02
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.86
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  253.73
 p-value of test no 203                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.93
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.36
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.77
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.01
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.85
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4299.02
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.73
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.45
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.42
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.30
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999869930
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.85
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999996308
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:31.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92110857.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56571
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.04
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.31
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.87
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.71
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.43
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.21
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.64
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.11
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.52
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.02
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.40
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.85
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.72
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4740.22
 p-value of test no 68                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908084
   j =  2                              :            45952
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908567
   j =  2                              :            45712
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 85                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.35
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.35
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.81
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.81
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.29
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.80
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.87
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.34
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17282.43
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.41
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.44
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.04
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.51
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.62
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.83
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.49
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.92
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.20
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.29
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.71
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.48
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.78
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.31
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.02
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.99
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.34
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.87
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.81
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.13
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.75
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.15
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.36
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.47
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.98
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.49
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.17
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.94
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.81
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.52
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.18
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.79
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4650.37
 p-value of test no 226                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.69
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.28
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.58
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.52
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.04
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000137575
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.48
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999734510
 
 Normal statistic for number of bits   :   -2.10
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:53.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93126665.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56572
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 12                 :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7108
 p-value of test no 18                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.02
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.23
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.79
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.14
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.67
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.81
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.40
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7243.38
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.14
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.58
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.22
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.95
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908714
   j =  2                              :            45637
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908258
   j =  2                              :            45862
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.67
 p-value of test no 78                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.89
 p-value of test no 119                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.32
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.18
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.12
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.37
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.80
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.11
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.29
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.35
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.63
 p-value of test no 136                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.92
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17440.73
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.52
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.58
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.56
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.12
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.94
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.29
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.37
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.45
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.69
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.71
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.71
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.20
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.82
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.48
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.49
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.28
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.42
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.15
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.83
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.88
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.23
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.88
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.59
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.59
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.66
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.99
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.72
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.97
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.41
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.60
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.60
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.72
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.51
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.64
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.30
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.12
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.20
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11501.41
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.61
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999885011
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.30
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000024868
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:29.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94175241.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56573
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    4.03
 p-value of test no 24                 :  8.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     973
 p-value of test no 25                 :  8.4e-3
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    3.86
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.52
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.36
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.85
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.05
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.24
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.16
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.59
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.86
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.94
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.14
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.83
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.61
 p-value of test no 67                 :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.91
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908222
   j =  2                              :            45886
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907905
   j =  2                              :            46037
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.87
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.01
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.63
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.73
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.97
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.70
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.35
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.27
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.44
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.21
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.24
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.89
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.01
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.86
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.81
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.92
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.97
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.64
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.83
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.67
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.72
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.20
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.64
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.53
 p-value of test no 159                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.75
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.45
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.14
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.28
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.66
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.75
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.04
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.00
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.50
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.32
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.77
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.10
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.69
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.77
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.86
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.67
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.05
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.12
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.96
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.78
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.78
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.43
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.35
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.51
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.26
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.66
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.25
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.20
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.93
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.18
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.13
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999924464
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.88
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000006874
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    2.69
 p-value of test no 244                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:54.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95158281.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56574
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 7                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 11                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9921
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.69
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.49
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.72
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.84
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.38
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.41
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.53
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.54
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.03
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.23
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.58
 p-value of test no 65                 :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.67
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.56
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.04
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907845
   j =  2                              :            46070
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.41
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.93
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.99
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.86
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.10
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9958
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.30
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.79
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.24
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.89
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.10
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.33
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.96
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.46
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.19
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.54
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.95
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.83
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.25
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.69
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.02
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.11
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.12
 p-value of test no 162                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.97
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.14
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.83
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.02
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.89
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.36
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.87
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.63
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.41
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.60
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.46
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.44
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.92
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.40
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.31
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.68
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.23
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.05
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.29
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.51
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.73
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.52
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.85
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.33
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.24
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.18
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000124048
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.00
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000089407
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:34.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96174089.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56575
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.04
 p-value of test no 23                 :  8.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.87
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.27
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.69
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.99
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.74
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.57
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.21
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.58
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.54
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.57
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.69
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.72
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.17
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.04
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908109
   j =  2                              :            45941
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907850
   j =  2                              :            46072
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.88
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.31
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.68
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.84
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.10
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.76
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.83
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.21
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.35
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17578.27
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.23
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.32
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.22
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.12
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.00
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.91
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.06
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.65
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.28
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.87
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.96
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.16
 p-value of test no 159                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.35
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.45
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.28
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.62
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.68
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.30
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.45
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.87
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.59
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.44
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.40
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.45
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.74
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.47
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.82
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.91
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.38
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.54
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.02
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.27
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.59
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.85
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9765.74
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9746.33
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.81
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.55
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.92
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.14
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.06
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.32
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.84
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999983279
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.08
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999846212
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9902
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:47.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97189897.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56576
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.92
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.40
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.86
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.30
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.65
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.55
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.32
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.82
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.14
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.64
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.23
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.13
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.81
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.14
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.32
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908842
   j =  2                              :            45573
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908539
   j =  2                              :            45723
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.96
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.24
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.46
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.32
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.85
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.55
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.46
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.00
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.04
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.00
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.25
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.50
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.81
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.19
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.51
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.58
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.74
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.75
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.23
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.47
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.62
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.97
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.59
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.67
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.94
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.31
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.17
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.57
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.58
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.93
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.37
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.78
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.07
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.01
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.26
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.25
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.46
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.45
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.21
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.07
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.71
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.40
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.88
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.58
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.03
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9912
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.24
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.60
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.38
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.57
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.89
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.47
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.08
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.24
 p-value of test no 231                :    0.9963
 
 
 -----------------------------------------------
 Total number of bits:  7999985181
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.13
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000134059
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:21.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98205705.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56577
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.92
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    4.48
 p-value of test no 44                 :  5.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.01
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.83
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.17
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.81
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.13
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.77
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.07
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.89
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.81
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.22
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.65
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.51
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908291
   j =  2                              :            45853
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907944
   j =  2                              :            46022
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.09
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.72
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.94
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.18
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.25
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.94
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.18
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.42
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.71
 p-value of test no 134                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.42
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17229.70
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.17
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.87
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.95
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.07
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.89
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.43
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.58
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.77
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.33
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.39
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.66
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.04
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.13
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.38
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.09
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.94
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.82
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.95
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.27
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.18
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.80
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.10
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.77
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.76
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.02
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.13
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.48
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.10
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.26
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.26
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.03
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.91
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.26
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.83
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.02
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.86
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.30
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.69
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.14
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.86
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.23
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999916472
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.53
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000245857
 
 Normal statistic for number of bits   :    1.94
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    2.68
 p-value of test no 254                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:45.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99221513.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56578
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     835
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.40
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.73
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.14
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.02
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.20
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.25
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.88
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.83
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.90
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.22
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.63
 p-value of test no 65                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.08
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.90
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45559
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869559
   j =  1                              :        399908884
   j =  2                              :            45555
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908117
   j =  2                              :            45937
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.31
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.57
 p-value of test no 120                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.86
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.17
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.72
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.58
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.55
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.68
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.18
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.60
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.87
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.85
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.62
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.52
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.15
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.92
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.83
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.71
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.48
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  594.93
 p-value of test no 158                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.03
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.34
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.10
 p-value of test no 161                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.55
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.26
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.44
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.47
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.84
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.12
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.89
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.79
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.30
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.93
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.07
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.94
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.72
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.01
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.96
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.91
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.04
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9777.06
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.39
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.96
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.55
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.79
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.28
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11566.85
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.02
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.52
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999921875
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.42
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000034828
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.052
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    2.07
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:57.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100270089.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56579
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997433
   j =  2                              :             1282
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5176
 p-value of test no 13                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4201
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.63
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.03
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.37
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.15
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.75
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.34
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.61
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.57
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6750.39
 p-value of test no 57                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.51
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.87
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.07
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.01
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.17
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908019
   j =  2                              :            45986
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 111                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.64
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.01
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.95
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.06
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.62
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.18
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.17
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17251.13
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.34
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.54
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.03
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.32
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.26
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.70
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.36
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.10
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.18
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.77
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.04
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.06
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.25
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.05
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.37
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.11
 p-value of test no 161                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.02
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  424.15
 p-value of test no 163                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.25
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.87
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.96
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.81
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.73
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.84
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.98
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.36
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.24
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.67
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.35
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.05
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.51
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.01
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.00
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.83
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.29
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.46
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.74
 p-value of test no 216                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.59
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.70
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.77
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.06
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.17
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.10
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.64
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000067237
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.01
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000087514
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:13.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101285897.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56580
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.63
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.46
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.18
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.73
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.15
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.21
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.18
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.19
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.23
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.53
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.56
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.18
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5160.05
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908139
   j =  2                              :            45926
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908152
   j =  2                              :            45921
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.00
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.98
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.56
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.18
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.91
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 130                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.73
 p-value of test no 133                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.53
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17646.64
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.43
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.77
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.28
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.29
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.91
 p-value of test no 150                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.17
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.09
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.20
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.46
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.96
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.37
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.83
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.05
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.40
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.69
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.52
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.25
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.66
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.70
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.64
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.21
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.82
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.24
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.88
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.92
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.56
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.17
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.88
 p-value of test no 175                :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.51
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.97
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.49
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.82
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.11
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.78
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.05
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.70
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.11
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.59
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12096.30
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.95
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.73
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000060250
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.08
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000143167
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.096
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:00.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82542611.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56581
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 12                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9975
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.48
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.26
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.69
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.69
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.78
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.74
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.11
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.19
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6762.71
 p-value of test no 57                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.50
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.33
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.03
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.01
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46324
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870324
   j =  1                              :        399907357
   j =  2                              :            46314
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908235
   j =  2                              :            45878
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-6
 p-value of test no 110                :    0.9966
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.30
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.90
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.62
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.13
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.37
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.37
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.99
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.64
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.96
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.58
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.81
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.52
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.32
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.64
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.38
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.22
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.50
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.24
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.41
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.83
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.08
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.44
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.02
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.77
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.98
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.91
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.72
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.68
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.30
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.75
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.57
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.11
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.70
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.13
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.16
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.58
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.16
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.59
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.15
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.08
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-3
 p-value of test no 200                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 202                :  2.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  272.12
 p-value of test no 203                :  5.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.12
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10271.46
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.85
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.59
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.55
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.25
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.18
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.05
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.81
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.20
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999967328
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.25
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999914174
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.86
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:48.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  88  PeriodsInStrings, r = 0         5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83296275.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56582
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.95
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9911
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.54
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.00
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.82
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.12
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7207.97
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.90
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.53
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.86
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.50
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.47
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907755
   j =  2                              :            46118
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908226
   j =  2                              :            45881
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
 p-value of test no 90                 :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  9.1e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  6.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.53
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.21
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.70
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.80
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.71
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.30
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.24
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   14.02
 p-value of test no 136                :  9.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.02
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.98
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.87
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.70
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.51
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.44
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.82
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.44
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.00
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.97
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.15
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.57
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.55
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.60
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.17
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.76
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.22
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.77
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.37
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.59
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.48
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.73
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.37
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.90
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.21
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.68
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.01
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.26
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.78
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.74
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.67
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.70
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.30
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.12
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.07
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.03
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.09
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5094.04
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.32
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.91
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.50
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.68
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.32
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.34
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000071509
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.90
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999988727
 
 Normal statistic for number of bits   :  -0.089
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.14e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:18.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              9.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84901907.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56583
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 33                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.98
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.25
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.04
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.15
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.22
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.91
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.40
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.77
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.74
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.49
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.51
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.60
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.71
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.97
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908259
   j =  2                              :            45866
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907733
   j =  2                              :            46129
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-5
 p-value of test no 113                :    0.9934
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.00
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.89
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.49
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.45
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.79
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.79
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.29
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.68
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.72
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17639.91
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.50
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.59
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.47
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.59
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.18
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.69
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.71
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.39
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.52
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.95
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.17
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.47
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.63
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.40
 p-value of test no 161                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.22
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.28
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   89.94
 p-value of test no 164                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.95
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.93
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.94
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.52
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.21
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.90
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.65
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.59
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.34
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.90
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.66
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.60
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.05
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.17
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.15
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.58
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.42
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.35
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.78
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.60
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.89
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.70
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.42
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.36
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000102046
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.12
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999948398
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 246                :    0.9936
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.66
 p-value of test no 248                :    0.9961
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:56.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85786643.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56584
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 11                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.64
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.50
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.12
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.36
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.82
 p-value of test no 53                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.08
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.48
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1308.42
 p-value of test no 56                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.34
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.87
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.57
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.69
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.35
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908624
   j =  2                              :            45682
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908287
   j =  2                              :            45852
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-5
 p-value of test no 109                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.83
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.47
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.87
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.15
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.64
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.79
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.55
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.52
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.94
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.95
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.57
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.70
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.36
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.27
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.36
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.98
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.29
 p-value of test no 155                :    0.9910
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.53
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.10
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.58
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.56
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.12
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.08
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.06
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.89
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.56
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.85
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.90
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.93
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.70
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.36
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.36
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.94
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.42
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.18
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.48
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.93
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.16
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.75
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.29
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.57
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.00
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.06
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.26
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.40
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.38
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.38
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.38
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.55
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.80
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.53
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.73
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999988712
 
 Normal statistic for number of bits   :  -0.089
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.56
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999975620
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:14.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86769683.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56585
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.19
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.85
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.49
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.27
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.10
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.51
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.41
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.97
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7235.32
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
 p-value of test no 59                 :    0.9965
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.85
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.72
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.78
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.06
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.80
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908105
   j =  2                              :            45940
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45426
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869426
   j =  1                              :        399909153
   j =  2                              :            45416
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.09
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.16
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.06
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.55
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.68
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.90
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.65
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.14
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 138                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   93.93
 p-value of test no 141                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17637.22
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.75
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.73
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.15
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.56
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.58
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.46
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.14
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.70
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.84
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.49
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.57
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.46
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.29
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.97
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.48
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.37
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.89
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.29
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.01
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.74
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.13
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.82
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.62
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.24
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.94
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.64
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.02
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.67
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.93
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.99
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.98
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.81
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.48
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.61
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4296.78
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.69
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.96
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.40
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.33
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999913544
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.64
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999977672
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:09.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87982099.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56586
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 45                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.82
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.36
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.83
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.22
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.50
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.08
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.00
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.55
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.62
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.38
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.61
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.17
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.51
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.36
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.19
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908277
   j =  2                              :            45854
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908025
   j =  2                              :            45980
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.71
 p-value of test no 117                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.87
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.66
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.72
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.13
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.95
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.77
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.00
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.63
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 138                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.70
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.45
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.77
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.42
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.00
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.60
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.65
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.48
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.28
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.09
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.82
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.82
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.48
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.77
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.73
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.73
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.64
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.82
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.58
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.72
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.15
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.83
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.82
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.80
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.90
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.90
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.58
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.26
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.17
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.94
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.75
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.83
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.86
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.53
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.13
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.17
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.78
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.36
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.23
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.15
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.75
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.32
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.34
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.87
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.81
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.16
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999961130
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.27
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000008062
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    2.25
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 253                :  8.9e-3
 
 Sample variance                       :    2.26
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:59.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88965139.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56587
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9918
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.83
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.23
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.76
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.70
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.21
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.73
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7291.39
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.40
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.15
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.94
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.60
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5249.70
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908054
   j =  2                              :            45967
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908685
   j =  2                              :            45656
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.68
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.93
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.92
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.10
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.33
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 128                :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.38
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.15
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.82
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.13
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.17
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.07
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.15
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.65
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.43
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.84
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.45
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.50
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.33
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.61
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.88
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.58
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.77
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.65
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.68
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.82
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.57
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.47
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.90
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.99
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.47
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.53
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.28
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.25
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.20
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.75
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.21
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.42
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.54
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.01
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.27
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.01
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.39
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.72
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.45
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.13
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.39
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.94
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.02
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.16
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.75
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12130.59
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.62
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000023254
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.25
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999888047
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:17.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89980947.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56588
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7041
 p-value of test no 15                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.07
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.66
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.53
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.38
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.94
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.87
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.74
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.15
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.42
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.44
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.50
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.56
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.61
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.30
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.66
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.23
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907842
   j =  2                              :            46070
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908245
   j =  2                              :            45873
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.44
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.08
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.38
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.16
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.04
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.03
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.46
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.50
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.89
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.82
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.31
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.23
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.91
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.10
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.53
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.80
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.89
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.60
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.42
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.04
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.51
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.32
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.47
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.57
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.77
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.88
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.62
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.56
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4770.43
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.86
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.77
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.29
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.26
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.72
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.05
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.31
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.65
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.21
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.82
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.69
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.99
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.25
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.01
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.91
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.35
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12147.61
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.06
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.98
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000128248
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.20
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000033691
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.20
 p-value of test no 244                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:50.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         0.9994 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90963987.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56589
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.75
 p-value of test no 22                 :  3.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9932
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.85
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.07
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.26
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.77
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.93
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.55
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1307.69
 p-value of test no 56                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6894.66
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.14
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.29
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.24
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.47
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908097
   j =  2                              :            45944
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908214
   j =  2                              :            45887
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.62e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.86
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.87
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.67
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.05
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.50
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.95
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.13
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.08
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.40
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.21
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.34
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.52
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.22
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.11
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.32
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.73
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.80
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.73
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.23
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.99
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.65
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.38
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.54
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.33
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.35
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.04
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.75
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.07
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.10
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.56
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.57
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.99
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.76
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.94
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.74
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.84
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.49
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.90
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.60
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.14
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.46
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.34
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.01
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.84
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.01
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.97
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.91
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.57
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.21
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000052309
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.36
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999995771
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:19.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91979795.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56590
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9917
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.94
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.67
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.61
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.60
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.30
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.64
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.41
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.30
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.97
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.18
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.69
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.72
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.74
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.23
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907818
   j =  2                              :            46088
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908754
   j =  2                              :            45617
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 84                 :    0.9959
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 92                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.19
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.97
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.42
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.49
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.15
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.47
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.79
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.68
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.29
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.18
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.99
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.67
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.44
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.74
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.28
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.75
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.77
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.00
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.04
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.06
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.06
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.60
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.26
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.42
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.16
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.32
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.95
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.79
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.16
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.00
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.45
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.82
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.19
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4772.41
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.01
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.51
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.00
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.23
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.13
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.68
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.14
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.25
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.58
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3854.33
 p-value of test no 227                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.17
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.41
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.35
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.18
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999955181
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.02
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000051904
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:00.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92995603.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56591
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    2.92
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.52
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9922
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.80
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.59
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.55
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.52
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.80
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.52
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.20
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.94
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.31
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.61
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.11
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.64
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.80
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908038
   j =  2                              :            45975
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46157
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870157
   j =  1                              :        399907687
   j =  2                              :            46155
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 84                 :  9.5e-4    *****
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 85                 :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.69
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.53
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.52
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.54
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.88
 p-value of test no 123                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.40
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.45
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.31
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.31
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.26
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.44
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.48
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.67
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.36
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.24
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.56
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.68
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.68
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.05
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.93
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.25
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.81
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.30
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.21
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.14
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.80
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.42
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.82
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.41
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.85
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.32
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.72
 p-value of test no 167                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.85
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.92
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.58
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.40
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.24
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.20
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.70
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.17
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.01
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.98
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.08
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.48
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.19
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.46
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.91
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.79
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.50
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.59
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.84
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.72
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.87
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000009163
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.93
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000063301
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:43.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93880339.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56592
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    3.47
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.07
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.30
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.45
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.52
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.51
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.60
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.04
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.96
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.20
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.65
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.55
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.62
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.99
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.34
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908330
   j =  2                              :            45832
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45522
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869522
   j =  1                              :        399908959
   j =  2                              :            45516
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    5.14
 p-value of test no 108                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.19
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.27
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.91
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.07
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.61
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.49
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.60
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.43
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.089
 p-value of test no 135                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 140                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.11
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17248.91
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.23
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.57
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.96
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.66
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.01
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.46
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.28
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.79
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.82
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.30
 p-value of test no 156                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.39
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.25
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.45
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.00
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.60
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.37
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.44
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.61
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.50
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.94
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.35
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.40
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.17
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.71
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.41
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.32
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.22
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.57
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.94
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.55
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.65
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.23
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.55
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.25
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.52
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3919.73
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.47
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.41
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.30
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000037483
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.23
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999916409
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:37.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94830611.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56593
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4171
 p-value of test no 14                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.29
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.13
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.59
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.50
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.62
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.97
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.89
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.60
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.26
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.43
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.44
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.17
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.15
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.47
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908445
   j =  2                              :            45773
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46179
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870179
   j =  1                              :        399907649
   j =  2                              :            46165
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.32
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.84
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.76
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.32
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.79
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.12
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.21
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.48
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.20
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.64
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17146.06
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.17
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.00
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.65
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.79
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.44
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.27
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.57
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.64
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.60
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.26
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.79
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.00
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.82
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.92
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.26
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.13
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.34
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.68
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.10
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.17
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.26
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.87
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.45
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.78
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.03
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.87
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.63
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.81
 p-value of test no 175                :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.75
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.13
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.72
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9650.40
 p-value of test no 215                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.93
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.84
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.52
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.35
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.36
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.16
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.63
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999857108
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.72
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000046165
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:09.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95813649.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56594
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5536
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.42
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.84
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.23
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.04
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.72
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.00
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.31
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.06
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.87
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.41
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.81
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.76
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908051
   j =  2                              :            45970
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908139
   j =  2                              :            45929
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 103                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.45
 p-value of test no 119                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.31
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.93
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.88
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.05
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.45
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.23
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.36
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.80
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17592.59
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.81
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.40
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.58
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.78
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.75
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.29
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.90
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.02
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.50
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.19
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.41
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.05
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.22
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.31
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.26
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.70
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.07
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.92
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.41
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.12
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.49
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.69
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.60
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.90
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.70
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.85
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.21
 p-value of test no 198                :    0.9966
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 201                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 202                :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  254.43
 p-value of test no 203                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.28
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.60
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.14
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.43
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.96
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.59
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.71
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.14
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.79
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.80
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000055183
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.02
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999817739
 
 Normal statistic for number of bits   :   -1.44
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:42.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96829457.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56595
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.50
 p-value of test no 34                 :  5.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.72
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.17
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.97
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.38
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.65
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.43
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.08
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.57
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6828.65
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.02
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.59
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.25
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.78
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908085
   j =  2                              :            45950
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907884
   j =  2                              :            46052
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
 p-value of test no 72                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.57
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.80
 p-value of test no 120                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.18
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.43
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.77
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.95
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.58
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.08
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.22
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17351.39
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.29
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.85
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.57
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.32
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.99
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.18
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.63
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.36
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.12
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.43
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.16
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.21
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.35
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.15
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.17
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.02
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.09
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.28
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.05
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.89
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.30
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.13
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.07
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.62
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.45
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.26
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.65
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.21
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.83
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.38
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.22e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.06
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.25
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.60
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.18
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.46
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.40
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.24
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.45
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.82
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.96
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.56
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.05
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.88
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000025828
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.60
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999985010
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9902
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:15.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97648657.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56596
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 3                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.22
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.53
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.34
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.12
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.15
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.14
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.12
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.92
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.99
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.67
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.78
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.03
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.55
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.99
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.61
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908403
   j =  2                              :            45791
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907929
   j =  2                              :            46031
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.12
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.56
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.62
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.10
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.75
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.50
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 138                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    5.67
 p-value of test no 140                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   83.17
 p-value of test no 141                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17676.24
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.72
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.74
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.06
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.88
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.89
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.16
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.26
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.24
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.67
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.80
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.30
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.65
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.08
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.44
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.59
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.97
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.34
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.59
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.22
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.41
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.38
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.24
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.16
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.11
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.26
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.98
 p-value of test no 175                :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.60
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.21
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.37
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.49
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.32
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.21
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.17
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.87
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.34
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4716.46
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.79
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.30
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12131.22
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.85
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.12
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000018442
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.61
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000020545
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:32.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98631697.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56597
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 11                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.40
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.22
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.03
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.77
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.95
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.43
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.37
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.77
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.87
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.63
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.95
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.03
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.85
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4908.67
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908326
   j =  2                              :            45837
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907922
   j =  2                              :            46033
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.50
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.96
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.96
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.03
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.32
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.84
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.45
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.51
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.02
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.68
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.09
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.69
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.71
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.74
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.76
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.19
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.63
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.80
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.11
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.01
 p-value of test no 159                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.71
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.89
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.58
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.87
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.82
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.78
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.70
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.47
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.03
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.36
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.57
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.67
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5208.89
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.25
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.22
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.12
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.85
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.60
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.29
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
 p-value of test no 204                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 206                :  8.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  263.32
 p-value of test no 207                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.26
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.24
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.50
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 223                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4674.82
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.49
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.49
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.90
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.37
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.21
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000109789
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.96
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999858029
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:29.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           5.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99614737.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56598
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.61
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     983
 p-value of test no 25                 :  3.3e-3
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.53
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.71
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.77
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.10
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.71
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.68
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.36
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.40
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.45
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.33
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.29
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.34
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.72
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.87
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908631
   j =  2                              :            45677
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46210
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870210
   j =  1                              :        399907586
   j =  2                              :            46198
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.45
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.91
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.55
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.20
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.77
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.87
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.39
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.68
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.79
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17263.16
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.60
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.80
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.95
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.39
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.38
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.10
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.62
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.59
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.18
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.92
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.84
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.77
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.95
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.26
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.06
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.70
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.23
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.17
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.26
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.57
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.31
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.22
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.99
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.02
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.94
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.55
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.07
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.46
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.32
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.40
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 201                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.74
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.61
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.10
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.33
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.84
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.44
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.85
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.87
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.48
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.88
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.10
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000056194
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.56
 p-value of test no 233                :  9.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000092662
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:32.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100663300.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56599
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 9                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9965
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.19
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.52
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.86
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.65
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.84
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.22
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.55
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.11
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6855.25
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.94
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.24
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.09
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.30
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.37
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908078
   j =  2                              :            45955
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908048
   j =  2                              :            45967
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 85                 :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.00
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.38
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.24
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.91
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.69
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.98
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17647.80
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.81
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.52
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.74
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.35
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.31
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.21
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.29
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.49
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.46
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.01
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.88
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.11
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.84
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.73
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.48
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.82
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.84
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.75
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.63
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.80
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.74
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.01
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.40
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.07
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.36
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.92
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.96
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.33
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.30
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 206                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  256.06
 p-value of test no 207                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.09
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.57
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.06
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.78
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.18
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.81
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.26
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11573.43
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.89
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999991865
 
 Normal statistic for number of bits   :  -0.064
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.95
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999951956
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:07.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               5.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101646340.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56600
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 9                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4150
 p-value of test no 14                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.55
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.52
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.99
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.83
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.24
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.05
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.08
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.31
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7274.99
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.99
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.86
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.55
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908553
   j =  2                              :            45716
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908565
   j =  2                              :            45713
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 77                 :    0.9958
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.76
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.24
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.53
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.68
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.57
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.80
 p-value of test no 125                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.30
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.41
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.31
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.70
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.85
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.95
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.48
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.63
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.52
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.25
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.24
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.60
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.25
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.77
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.55
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.70
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.20
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.03
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.77
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.81
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.54
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.14
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.34
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.04
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.98
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.15
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.34
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.57
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.47
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.56
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.11
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.16
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.47
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.33
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.52
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.03
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.85
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.04
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.19
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.11
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.43
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.22
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.96
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.99
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.94
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999964643
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.15
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999984893
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:20.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82575380.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56601
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 5                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 6                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.07
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.41
 p-value of test no 48                 :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.08
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.79
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.77
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.25
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.90
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.83
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.18
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.39
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.82
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.70
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.07
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.21
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.91
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45701
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908602
   j =  2                              :            45693
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907883
   j =  2                              :            46057
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.68
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.57
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.03
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.52
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.28
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.72
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.47
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.57
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.08
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17786.05
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.16
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.45
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.51
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.27
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.69
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.50
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.56
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.29
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.02
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.64
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.34
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.92
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.72
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.47
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.44
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.05
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.77
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.70
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.73
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.22
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.49
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.13
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.27
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.94
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4758.66
 p-value of test no 173                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.71
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.70
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.67
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.47
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.50
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.42
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.09
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9690.27
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.81
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.06
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.98
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.74
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.34
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.76
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.84
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.24
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999924527
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.27
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999945290
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    2.36
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:38.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83787796.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56602
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5567
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7540
 p-value of test no 18                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.47
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.13
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.27
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.88
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.40
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.72
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7281.76
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.09
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.50
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.55
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.92
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.06
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908664
   j =  2                              :            45662
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45610
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869610
   j =  1                              :        399908781
   j =  2                              :            45608
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.60
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.37
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.72
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.26
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.22
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.77
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.47
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.86
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.41
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.77
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.35
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.76
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.20
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.65
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.97
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.57
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.79
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.48
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.16
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.12
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.04
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.24
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.99
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.95
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.93
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.42
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.74
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.20
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.32
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.47
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.36
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.18
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.57
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.38
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.31
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.98
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.18
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.75
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.29
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.61
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.10
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.28
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.58
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.56
 p-value of test no 218                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.35
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-4
 p-value of test no 223                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5135.30
 p-value of test no 226                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.68
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.96
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.27
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.68
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.94
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000039079
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.55
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000133810
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:01.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84836372.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56603
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    3.26
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.11
 p-value of test no 40                 :  8.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.33
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.83
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   26.93
 p-value of test no 53                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.53
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.52
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.32
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7356.25
 p-value of test no 57                 :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.68
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.29
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.72
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.50
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.77
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908022
   j =  2                              :            45983
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908065
   j =  2                              :            45966
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.58
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.28
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.84
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.80
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.18
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.36
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.47
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.93
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.07
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.38
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.36
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.49
 p-value of test no 148                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.03
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.82
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.23
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.94
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.44
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.96
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.88
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.48
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.39
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.19
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.37
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.25
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.26
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.09
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.06
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.17
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.76
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.15
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.44
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.91
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.62
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.36
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.57
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.87
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.28
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.83
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.96
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.41
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.16
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.19
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.45
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.32
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.05
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4266.44
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.85
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.43
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.76
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000009223
 
 Normal statistic for number of bits   :   0.073
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.15
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999918152
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:08.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  33  CouponCollector, r = 27         0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85950484.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56604
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    5.03
 p-value of test no 30                 :  2.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     529
 p-value of test no 31                 :    0.9983
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.55
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.92
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.63
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.17
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.09
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.08
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.61
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.40
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.35
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.15
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.43
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.58
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.34
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.40
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.73
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908221
   j =  2                              :            45882
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907869
   j =  2                              :            46061
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.83
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.48
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.94
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.35
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.93
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.49
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.95
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.01
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17164.06
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.47
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.31
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.25
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.54
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.29
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.14
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.10
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.61
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.29
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.53
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.79
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.31
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.39
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.97
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.87
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.85
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.54
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.92
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.62
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.21
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.74
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.82
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.09
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.50
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.39
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.49
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.02
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.49
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.50
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.62
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.18
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.91
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.00
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.04
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.80
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.32
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.41
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.39
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.52
 p-value of test no 231                :  4.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000038626
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.73
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000029770
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:59.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86966292.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56605
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 11                 :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.24
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.63
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.56
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.15
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.00
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.37
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.41
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.86
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.97
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.64
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.22
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.27
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.64
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.43
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.95
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.38
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908186
   j =  2                              :            45904
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908482
   j =  2                              :            45753
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 73                 :    0.9923
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 106                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 108                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.52
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.33
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.89
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.02
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.51
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.29
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.76
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.76
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.87
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.10
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.00
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.35
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.58
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.28
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.48
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.36
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.07
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.17
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.78
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.62
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.46
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.70
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.61
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.89
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.30
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.31
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.18
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.55
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.65
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.39
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.86
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.89
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.45
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.24
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.70
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.94
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.79
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.35
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.90
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.48
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.64
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.66
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.75
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.78
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.69
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.53
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.52
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.72
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000103039
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.55
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999874805
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.047
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:31.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87949332.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56606
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 24                 :    0.9976
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.84
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.17
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.58
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.06
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.85
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.09
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.77
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.99
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.21
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.82
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.49
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5345.71
 p-value of test no 68                 :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907687
   j =  2                              :            46152
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908472
   j =  2                              :            45758
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.46
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.82
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.48
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.16
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.80
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.99
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.89
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.48
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.65
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.83
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.52
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.07
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.22
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.69
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.34
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.69
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.16
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.48
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.58
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.37
 p-value of test no 160                :  3.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.32
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.32
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.49
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.53
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.88
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.41
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.73
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.31
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.76
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.90
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.53
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.78
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.72
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.99
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.90
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.01
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.29
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.32
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.48
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.52
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.47
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.05
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.12
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.16
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.16
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.96
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.61
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999984179
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.80
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000031129
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:13.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88932372.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56607
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.05
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.85
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.28
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.94
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.21
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.14
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.78
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.30
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.74
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.63
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.26
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.45
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46193
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870193
   j =  1                              :        399907620
   j =  2                              :            46181
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908084
   j =  2                              :            45949
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-4
 p-value of test no 109                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 111                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 114                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.93
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.75
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.52
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.44
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.67
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.85
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.75
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.48
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.39
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.07
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17708.24
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.67
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.56
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.65
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.69
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.09
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.22
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.36
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.99
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.70
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.64
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.42
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.72
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.67
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.33
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.46
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.00
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.80
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.58
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.73
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.89
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.22
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.88
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.82
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.33
 p-value of test no 172                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.77
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.55
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.00
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.09
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.24
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.99
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.11
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.61
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.84
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.82
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.93
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.46
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.68
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.56
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.32
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.46
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999990746
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.81
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999987605
 
 Normal statistic for number of bits   :  -0.098
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-3
 p-value of test no 246                :    0.9973
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 248                :    0.9940
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:19.73
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89948180.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56608
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.93
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.07
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.17
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.26
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.57
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.74
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.05
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.53
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.63
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.94
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.36
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.66
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.60
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.99
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908713
   j =  2                              :            45636
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46111
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870111
   j =  1                              :        399907785
   j =  2                              :            46097
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.05
 p-value of test no 115                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.43
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.89
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.82
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.89
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.22
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.34
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 127                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.64
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.90
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.61
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17585.90
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.34
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.41
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.04
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.70
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.84
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.84
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.71
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.28
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.10
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.88
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.40
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.72
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.03
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.12
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.87
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.49
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.79
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.05
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.72
 p-value of test no 167                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.38
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.63
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.32
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.12
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.45
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4658.40
 p-value of test no 173                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.23
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.08
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.52
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.67
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.91
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.80
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.96
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.17
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.57
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5125.65
 p-value of test no 222                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.76
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.66
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.30
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12106.05
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.55
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.92
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000130969
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.82
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999943214
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:20.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91029524.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56609
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.86
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.10
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.35
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.28
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.74
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.12
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.10
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.73
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.61
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.88
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.96
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.37
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.91
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.03
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.85
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908125
   j =  2                              :            45936
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46173
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907657
   j =  2                              :            46167
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.78
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.80
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.29
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.56
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.04
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.10
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   22.90
 p-value of test no 134                :  4.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.94
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.86
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.03
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.09
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.41
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.04
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.63
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.85
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.39
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.74
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.59
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.88
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.82
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.44
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.41
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.78
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.38
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.33
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.57
 p-value of test no 163                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.55
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.40
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.54
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.05
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4822.39
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.69
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.91
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.89
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.66
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.16
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.28
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.81
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.81
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.08
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.89
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.06
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.44
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.33
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.74
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.19
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.42
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.97
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.35
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12095.50
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.39
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000114676
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.28
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999849422
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.12
 p-value of test no 244                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:43.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         4.2e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92045332.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56610
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.88
 p-value of test no 35                 :  1.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.15
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.63
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.61
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.53
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.02
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.23
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.26
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.65
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.88
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.58
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.56
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46382
 p-value of test no 70                 :  9.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870382
   j =  1                              :        399907242
   j =  2                              :            46370
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908068
   j =  2                              :            45963
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.24
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.64
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.50
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.26
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.02
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.06
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.92
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.91
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.24
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.83
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.10
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.51
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.64
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.58
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.15
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.97
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.41
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.68
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.95
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.84
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.94
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.32
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.11
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.78
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.76
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.32
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.78
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.18
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.01
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.98
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.84
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.11
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.15
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.13
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.15
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.78
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.72
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.10
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.98
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.59
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.05
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.83
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.23
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.51
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.19
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 219                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.52
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.64
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.34
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.61
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.63
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.20
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.57
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999836744
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.79
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000114229
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 246                :    0.9918
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:05.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93061140.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56611
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5568
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7124
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.01
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.88
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.61
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.27
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.06
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.25
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.85
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.06
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.11
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.97
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.23
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.25
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.73
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.08
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908850
   j =  2                              :            45572
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908689
   j =  2                              :            45651
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.18
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.04
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.95
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.18
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.62
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.68
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.89
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.23
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.42
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 144                :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16925.12
 p-value of test no 145                :    0.9968
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.71
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.93
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.64
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.69
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.41
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   64.83
 p-value of test no 152                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.51
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.28
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.36
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.30
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.55
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.94
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.07
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.47
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.03
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.48
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.12
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.00
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.10
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.19
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.15
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.97
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.73
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.64
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.20
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.23
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.04
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.46
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.00
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.56
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.32
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.55
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.37
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.47
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.42
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.32
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.52
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.86
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12118.85
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.12
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.12
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000008608
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.56
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999969497
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:39.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94076948.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56612
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     836
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    3.38
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9912
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.42
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    2.74
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.71
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.90
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.28
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.75
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.78
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.71
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.83
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.82
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.93
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.12
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.29
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.42
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.06
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908303
   j =  2                              :            45841
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907771
   j =  2                              :            46110
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.68
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.89
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.55
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.87
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.81
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.18
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.98
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 130                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.15
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.11
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17441.64
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.98
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.85
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.43
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.19
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.90
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.03
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.96
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.68
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.89
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.51
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.49
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.16
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.43
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.40
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.43
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.26
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.89
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.44
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.87
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.08
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.26
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.66
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.47
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.14
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.29
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4820.86
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.91
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.64
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.66
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.76
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.73
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.63
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.83
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.60
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.05
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.05
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.27
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.31
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.96
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.38
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.37
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999900044
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.02
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000136561
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.14e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:10.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95059988.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56613
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    4.07
 p-value of test no 27                 :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.03
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.28
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.18
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.30
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.41
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  362.58
 p-value of test no 55                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.07
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.79
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.32
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.78
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.84
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.32
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908058
   j =  2                              :            45968
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907897
   j =  2                              :            46050
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.58
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.31
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.56
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.12
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.55
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.14
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.61
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.23
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.67
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.06
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.54
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.24
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.23
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.37
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.45
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.91
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.36
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.37
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.33
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.26
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.98
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.14
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.43
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.82
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.20
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.00
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.79
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.85
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.81
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.26
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.62
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.84
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.81
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.37
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.43
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.64
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.37
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.07
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.76
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.42
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.22
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 209                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 210                :  8.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10339.54
 p-value of test no 211                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.23
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.19
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.08
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.31
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.75
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.13
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.26
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.44
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999971249
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.16
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000001687
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 241                :    0.9903
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.35
 p-value of test no 243                :    0.9907
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:26.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96075796.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56614
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5268
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.48
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.48
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.33
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.62
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.32
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.61
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.18
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.87
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.43
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.43
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.68
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.58
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.32
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.93
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907972
   j =  2                              :            46011
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908563
   j =  2                              :            45711
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.85
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.52
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.36
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.86
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.76
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.25
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.91
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 128                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.17
 p-value of test no 129                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.29
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.72
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.14
 p-value of test no 135                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.84
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17375.37
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.80
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.27
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.69
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.47
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.22
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.96
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.11
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.43
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.60
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.24
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.90
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.48
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.00
 p-value of test no 160                :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.89
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  591.02
 p-value of test no 163                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.02
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.09
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.07
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.28
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.33
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.55
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.51
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.92
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4775.94
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.24
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.21
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.07
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 190                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.35
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.33
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.41
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10229.65
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.54
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.71
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.73
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.51
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.65
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.01
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.90
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.09
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999974444
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.11
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999976865
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9965
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:27.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97058836.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56615
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997181
   j =  2                              :             1408
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.58
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.70
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.08
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.13
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.93
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.11
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.51
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.83
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.71
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.70
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45603
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869603
   j =  1                              :        399908796
   j =  2                              :            45599
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908080
   j =  2                              :            45957
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.85
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.23
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.40
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.02
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.06
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.35
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.29
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.23
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.20
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17375.48
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.41
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.84
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.30
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.29
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.47
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.86
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.73
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.37
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.22
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.38
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.71
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.80
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.17
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.75
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.16
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.83
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.02
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.92
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.39
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.37
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.49
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.54
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.79
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.79
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.66
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.99
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.98
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.17
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.37
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.43
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.96
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.08
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.01
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.35
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5101.92
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.63
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.08
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.79
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.77
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000026644
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.90
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999860201
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:52.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98041876.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56616
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 30                 :    0.9962
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.78
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.27
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.08
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.98
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.71
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.64
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.49
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.45
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.95
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.39
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.96
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.60
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.21
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46191
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870191
   j =  1                              :        399907621
   j =  2                              :            46185
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907826
   j =  2                              :            46084
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.80
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.48
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.41
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.18
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.61
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.87
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.51
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.42
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.60
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.85
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17454.18
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.53
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.33
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.53
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.81
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.55
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.20
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.18
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.69
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.00
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.95
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.29
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.93
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.29
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.97
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.81
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.51
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.76
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.89
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.53
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.20
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.16
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.94
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.25
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.54
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.35
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.35
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.20
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.76
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.41
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.16
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.61
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.02
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9689.24
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 217                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.90
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.21
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.57
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4346.53
 p-value of test no 228                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.55
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.05
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.43
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999821009
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.89
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000132484
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:34.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99155988.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56617
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.89
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 24                 :    0.9981
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    3.46
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.99
 p-value of test no 40                 :  3.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.80
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.30
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.65
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.83
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.24
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.92
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.26
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.41
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.47
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.21
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.07
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.78
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.55
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908266
   j =  2                              :            45864
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908559
   j =  2                              :            45713
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.00
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.02
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.74
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.83
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.23
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.53
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.56
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.41
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.20
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 143                :    0.9922
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17036.46
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.36
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.45
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.91
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.16
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.84
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.67
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.39
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.57
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.15
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.64
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.42
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.21
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.27
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.90
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.87
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.34
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.84
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.43
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.28
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.30
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.77
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.00
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.08
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.94
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.55
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.06
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.45
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.23
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.58
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.52
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.05
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.06
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.46
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.32
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.40
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.88
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.24
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.69
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.92
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.85
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999781478
 
 Normal statistic for number of bits   :   -1.73
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.11
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999769277
 
 Normal statistic for number of bits   :   -1.82
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:51.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100139028.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56618
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 3                  :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    3.24
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    4.08
 p-value of test no 39                 :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.97
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.18
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.00
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.73
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.36
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.10
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.60
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.01
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.90
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.74
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.96
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.68
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.31
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.67
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45536
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869536
   j =  1                              :        399908931
   j =  2                              :            45530
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908743
   j =  2                              :            45621
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.37
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.57
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.66
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.38
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.86
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.35
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.77
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.09
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17588.95
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.17
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.64
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.09
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.08
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.33
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.67
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.71
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.14
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.36
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.38
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.66
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.81
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.50
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.22
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.69
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.44
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.97
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.53
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.79
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.72
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.04
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.15
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.85
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.24
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.29
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.84
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4740.71
 p-value of test no 173                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.10
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.94
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.19
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.39
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.45
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.95
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.70
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.39
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.67
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.73
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.83
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.39
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.85
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.42
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.59
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999926327
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.84
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000149752
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:55.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101187604.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56619
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 11                 :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7097
 p-value of test no 20                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    5.33
 p-value of test no 30                 :  2.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.42
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.91
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.68
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.00
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.87
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.57
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.55
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.59
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.86
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.48
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.26
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.80
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.34
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.79
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908088
   j =  2                              :            45950
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907762
   j =  2                              :            46113
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.17
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.99
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.01
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.70
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.47
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.18
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.70
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.85
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.65
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.43
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17127.83
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.45
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.73
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.70
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.82
 p-value of test no 151                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.07
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.37
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.56
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.80
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.13
 p-value of test no 158                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.00
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.29
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.46
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.55
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.32
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.86
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.10
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.91
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.34
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4753.98
 p-value of test no 168                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.48
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.79
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.07
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.25
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.28
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.78
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.12
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.38
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.24
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.19
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.40
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.04
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.91
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.17
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.67
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.21
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.38
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.54
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.59
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000079741
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.64
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000068176
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:28.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9990 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102137876.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56620
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997427
   j =  2                              :             1285
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.29
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.75
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.52
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.26
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.82
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.11
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.41
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.04
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.53
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.45
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.76
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.41
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.32
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.35
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.38
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45394
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869394
   j =  1                              :        399909213
   j =  2                              :            45392
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908245
   j =  2                              :            45876
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-5
 p-value of test no 110                :    0.9918
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.53
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.51
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.45
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.89
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.31
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.53
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.34
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.65
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.83
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.02
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17059.73
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.22
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.20
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.32
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.27
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.20
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.80
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.63
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.78
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.79
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.70
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.47
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.90
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.85
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.40
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.89
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.31
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.58
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.16
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4818.45
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.17
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.12
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.30
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.02
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.33
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.09
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.21
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.21
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.49
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.01
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.99
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.25
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.87
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.30
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.36
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.49
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.56
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.45
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.24
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.72
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.60
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000017650
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.25
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000059401
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.28
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:39.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82608149.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56621
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    3.99
 p-value of test no 27                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.88
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.40
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.70
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.35
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.88
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.44
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.33
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.78
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.93
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.88
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.36
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.86
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.07
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907810
   j =  2                              :            46086
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908892
   j =  2                              :            45548
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
 p-value of test no 84                 :    0.9956
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
 p-value of test no 93                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.88
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.55
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.96
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.58
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.49
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.60
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.05
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.40
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.20
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 144                :  6.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17839.38
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.12
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.49
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.95
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.10
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.85
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.19
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.61
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.81
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.05
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.91
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.28
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.66
 p-value of test no 161                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.55
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.04
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.61
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.25
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.12
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.82
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.62
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.20
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.49
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.56
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.69
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.56
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.64
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.35
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.62
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    2.20
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.96
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.21
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.48
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.58
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.35
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.54
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.80
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3911.22
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.12
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.28
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.13
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.95
 p-value of test no 231                :  8.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000040552
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.83
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999891419
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    2.40
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:50:42.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83001365.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56622
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.42
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.03
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.53
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.40
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.25
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.21
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.93
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.88
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.73
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.60
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.48
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.26
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.57
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5250.81
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46129
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870129
   j =  1                              :        399907745
   j =  2                              :            46123
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908401
   j =  2                              :            45792
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 88                 :    0.9958
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.92
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.30
 p-value of test no 120                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.81
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.64
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.75
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   69.26
 p-value of test no 125                :  3.8e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.74
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.02
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.91
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17249.12
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.61
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.81
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.60
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.99
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.99
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.36
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.24
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.23
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.01
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.58
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.81
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.06
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.07
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.60
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.13
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.16
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.28
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.20
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.95
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.84
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.17
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.61
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.26
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.91
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.32
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.77
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.30
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.15
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.65
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :7.02e-17
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-4
 p-value of test no 193                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.74
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.07
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.05
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.16
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.050
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.72
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.02
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.41
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.42
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.81
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.26
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.90
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000128353
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.51
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999971345
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.19
 p-value of test no 249                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:48.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    3.8e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84934677.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56623
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.9901
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.41
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.26
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.55
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.71
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.77
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.03
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.29
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.79
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.54
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.21
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.27
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.41
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4917.65
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908394
   j =  2                              :            45797
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908255
   j =  2                              :            45868
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.62
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.25
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.66
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.72
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.33
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.96
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.35
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.37
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 139                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.83
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.91
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.18
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.50
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.25
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.31
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.06
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.97
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.97
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.96
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.52
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.52
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.84
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.90
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.31
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.40
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.35
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.52
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.13
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.04
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5200.44
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.62
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.11
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.98
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.58
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.76
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.88
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.32
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.90
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.28
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.38
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.65
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.19
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.62
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.94
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.80
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.29
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.95
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.80
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.98
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.06
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999916025
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.59
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999964736
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:16.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85917717.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56624
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.39
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.48
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.56
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.80
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.88
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.17
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.92
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7292.47
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.55
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.56
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.53
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.22
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908096
   j =  2                              :            45952
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45378
 p-value of test no 71                 :    0.9904
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869378
   j =  1                              :        399909244
   j =  2                              :            45378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 104                :    0.9917
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.67
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.41
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.67
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.40
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.38
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.97
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.73
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.94
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.31
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.61
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17655.04
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.09
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.48
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.05
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.46
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.44
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.49
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.45
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.67
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.72
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.79
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.38
 p-value of test no 156                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.53
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.01
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.63
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.64
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.16
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.42
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.88
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.68
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.70
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.70
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.68
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.24
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.72
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.89
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.45
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.40
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.22
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.48
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.16
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.50
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.69
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.16
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.61
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.70
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.26
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.70
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.08
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.99
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.88
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.01
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999966074
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.17
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999874052
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:36.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86900757.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56625
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    4.91
 p-value of test no 27                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.66
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   39.32
 p-value of test no 48                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.41
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.51
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.48
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.99
 p-value of test no 53                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.84
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.44
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.62
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7156.40
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.48
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.37
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.45
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5287.76
 p-value of test no 68                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45290
 p-value of test no 70                 :    0.9971
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869290
   j =  1                              :        399909421
   j =  2                              :            45288
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908569
   j =  2                              :            45711
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 104                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.70
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   32.96
 p-value of test no 121                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.19
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.15
 p-value of test no 123                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.84
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.40
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.98
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.92
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17206.15
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.67
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.19
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.54
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.88
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.59
 p-value of test no 153                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.09
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.99
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.33
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.75
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.96
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.59
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.02
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.92
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.12
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.49
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  113.53
 p-value of test no 165                :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.44
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.51
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.99
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.11
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.04
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.04
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.94
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.08
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.68
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.82
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.56
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.38
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.92
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.37
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.55
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.78
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.28
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.11
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.97
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.59
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.96
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.81
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12071.22
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.86
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000067531
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.33
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000074887
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    2.62
 p-value of test no 239                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:53.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  61  WeightDistrib, r = 28           0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87883797.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56626
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    3.92
 p-value of test no 24                 :  9.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    4.49
 p-value of test no 26                 :  5.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.47
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.77
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.09
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.56
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.33
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   93.41
 p-value of test no 53                 :  7.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.38
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.74
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.37
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.57
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.99
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.44
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  164.09
 p-value of test no 67                 :  3.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5191.95
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908265
   j =  2                              :            45860
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908585
   j =  2                              :            45706
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.39
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.50
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.84
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.10
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.68
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.03
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.32
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.78
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.30
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.65
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.38
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.08
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.71
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.40
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.36
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.34
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.99
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.82
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.58
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.29
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.72
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.43
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.85
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.85
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.69
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.11
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.56
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.23
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.27
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.11
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.92
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.10
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.38
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.82
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.60
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.86
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.83
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.22
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.57
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.49
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.17
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.56
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.61
 p-value of test no 218                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.24
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.94
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.27
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.69
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.22
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.94
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.33
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999793373
 
 Normal statistic for number of bits   :   -1.63
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000029932
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 247                :  6.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.72
 p-value of test no 248                :  3.3e-3
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:52.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  33  CouponCollector, r = 27         7.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88834069.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56627
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 3                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997245
   j =  2                              :             1376
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.98
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.51
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.84
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.46
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.71
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.14
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.11
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.53
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.77
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.86
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.22
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.49
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907964
   j =  2                              :            46012
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908638
   j =  2                              :            45675
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-5
 p-value of test no 109                :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 111                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.29
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.57
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.52
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.03
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.27
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.18
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.92
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.13
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.92
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.92
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.20
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.12
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.51
 p-value of test no 147                :    0.9900
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.76
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.18
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.84
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.86
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.45
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.97
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.87
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.97
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.93
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.60
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.19
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.43
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.52
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.46
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.24
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.37
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.66
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.25
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.18
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.07
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.56
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.51
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.63
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.32
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.14
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.94
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.54
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.88
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.04
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.26
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.46
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9937
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.67
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.86
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 218                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.36
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.82
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.54
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.31
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.75
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.22
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.83
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999955826
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.79
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000040882
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:08.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89849877.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56628
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4178
 p-value of test no 16                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9912
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.06
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.98
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.36
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.26
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.18
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.13
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.52
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.52
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.64
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.58
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.23
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.14
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.92
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.67
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.17
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.06
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5204.48
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908054
   j =  2                              :            45970
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908321
   j =  2                              :            45829
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.29
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.77
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.60
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.19
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.79
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.64
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.66
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.51
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.04
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.96
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.22
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.24
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.45
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.08
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.36
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.79
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.71
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.52
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.13
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.30
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.02
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.88
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.98
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.80
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.34
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  119.47
 p-value of test no 160                :  6.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.14
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.63
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.01
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.43
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.14
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.42
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.74
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.91
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.92
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.52
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.20
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.21
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.62
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.98
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.84
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.25
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.72
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.46
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 209                :    0.9921
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9749.17
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.06
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.35
 p-value of test no 218                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.59
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.61
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.47
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.10
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.46
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.71
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.73
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999985931
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.84
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000072637
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:51.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     6.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90931221.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56629
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    3.48
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     975
 p-value of test no 25                 :  7.0e-3
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.25
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.95
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.31
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.57
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.22
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.18
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.39
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.99
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.94
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.00
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.15
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.41
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.35
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908323
   j =  2                              :            45825
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908545
   j =  2                              :            45723
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.49
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.07
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.26
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.91
 p-value of test no 122                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.73
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.96
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.82
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.07
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.31
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17811.41
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.73
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.51
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.00
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.89
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.52
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.41
 p-value of test no 151                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.21
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.20
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.59
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.40
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.27
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.26
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.29
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.23
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.47
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.17
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.38
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.80
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.38
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.26
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.09
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.01
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.22
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.54
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.44
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.13
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.29
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.52
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.09
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.77
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.79
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.86
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.98
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
 p-value of test no 208                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10330.32
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.82
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.80
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.92
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.41
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.31
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.38
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.54
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.94
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999872246
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.55
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000081745
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:07.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91848725.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56630
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4174
 p-value of test no 14                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.09
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.24
 p-value of test no 47                 :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.18
 p-value of test no 48                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.86
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.22
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.82
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.12
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.07
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.78
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.87
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.81
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.43
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.19
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.75
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.25
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907765
   j =  2                              :            46113
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908545
   j =  2                              :            45723
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 116                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.94
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.77
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.66
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.13
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.57
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.14
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.97
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.29
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.78
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.53
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.15
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17141.82
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.84
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.80
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.85
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.72
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.36
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.43
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.42
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.50
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.60
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.93
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.78
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.35
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.87
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.96
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.41
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.63
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.79
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.33
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.37
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.62
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.74
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.64
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.98
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.31
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.36
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.56
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.91
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.31
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.74
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.08
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.03
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.35
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.15
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.14
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10222.68
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.13
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.40
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.16
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.03
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.50
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.51
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.44
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.67
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999991751
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.31
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000015382
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:35.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92930055.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56631
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 10                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   41.75
 p-value of test no 48                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.88
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.81
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.31
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.84
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.19
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.18
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.32
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7207.30
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.98
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.01
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.44
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.98
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.52
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908089
   j =  2                              :            45954
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907749
   j =  2                              :            46121
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.22
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.91
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.91
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.46
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.22
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.20
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.76
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.99
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.75
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.03
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.64
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.67
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.26
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.61
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.06
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.75
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.52
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.27
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.38
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.80
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.19
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.94
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.34
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.39
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.39
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.84
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.17
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.19
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.40
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.64
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.54
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.66
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.12
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.91
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.52
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.24
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.12
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 186                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.81
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.61
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.97
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.00
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.76
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.42
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.10
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.09
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.93
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.57
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.50
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.71
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000115213
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.49
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000036748
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:28.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93814791.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56632
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7080
 p-value of test no 20                 :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.34
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.62
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.74
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.42
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.82
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.28
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.76
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.64
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.84
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.81
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.90
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.93
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.31
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.74
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.70
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.00
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.13
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907887
   j =  2                              :            46049
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908174
   j =  2                              :            45907
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.92
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.52
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.68
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.34
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.62
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.18
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.58
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.95
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.46
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.58
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.88
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.94
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.44
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.39
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.56
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.25
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.16
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.56
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.22
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.17
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.21
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.92
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.96
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.26
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.95
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.46
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.84
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.46
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.63
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.94
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.26
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.19
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.04
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.22
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.39
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.35
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.84
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.99
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.15
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.93
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.98
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.18
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 210                :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.94
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.19
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.81
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.58
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.84
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.20
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.40
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.38
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.47
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999987530
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.85
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999988823
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9902
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.10
 p-value of test no 254                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:33.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94994439.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56633
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    3.66
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.24
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.32
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.10
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.13
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.85
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.17
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.71
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.83
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.15
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7248.45
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.30
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.40
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.49
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.27
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.98
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908423
   j =  2                              :            45787
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.73
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.26
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.81
 p-value of test no 123                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.60
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.99
 p-value of test no 125                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.69
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 130                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.17
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.93
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.70
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17817.20
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.58
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.81
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.15
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.84
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.42
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.52
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.42
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.89
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.57
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.56
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.60
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.97
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.11
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.31
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.60
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.68
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.66
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.15
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.21
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.68
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.11
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.20
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.23
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.72
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.20
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.10
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.15
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.66
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.87
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.33
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.33
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.08
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.00
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.23
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.07
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.68
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.87
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.18
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.70
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12055.99
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.36
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.80
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999887942
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.23
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999881189
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 250                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 252                :  9.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 253                :    0.99
 
 Sample variance                       :    2.15
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:02.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95911943.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56634
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    3.96
 p-value of test no 30                 :  9.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.62
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.88
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.59
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.10
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.96
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.68
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.59
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.83
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7195.86
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.71
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.12
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.03
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.07
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5218.93
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908736
   j =  2                              :            45626
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908516
   j =  2                              :            45739
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.12
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.84
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.37
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.64
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.67
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.69
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.18
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.17
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.83
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.66
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.27
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.94
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.64
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.55
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.30
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.58
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.29
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.22
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.84
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.10
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.82
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.03
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.36
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.92
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.32
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.33
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.55
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.21
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.50
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.03
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.86
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.10
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.42
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5142.65
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.38
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.17
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.30
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.43
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.34
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.98
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.20
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4706.22
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.67
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.99
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.89
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.64
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.18
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000001678
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.18
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999990323
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:53.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96927751.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56635
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7568
 p-value of test no 15                 :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.77
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.13
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.70
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.31
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.97
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.60
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.92
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.76
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.01
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.00
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.74
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.93
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.30
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.66
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46181
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870181
   j =  1                              :        399907638
   j =  2                              :            46181
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908148
   j =  2                              :            45920
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.06
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.46
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.17
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.52
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.54
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.81
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.63
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.95
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.41
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.02
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.59
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.03
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.03
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.24
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.05
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.27
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.10
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.82
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.23
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  190.58
 p-value of test no 159                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.56
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.62
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.04
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.17
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.21
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.14
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.73
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.86
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.36
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.08
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.97
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.70
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.40
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.97
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.87
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.35
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.47
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.68
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.59
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.58
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.10
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.20
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.55
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.36
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.17
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.95
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.57
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.63
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.05
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.52
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000214312
 
 Normal statistic for number of bits   :    1.69
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.57
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999961541
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    2.00
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    2.03
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:15.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97943559.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56636
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.18
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.46
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.59
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.04
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.12
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.64
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.65
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.23
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 62                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.69
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.95
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.84
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.20
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908339
   j =  2                              :            45826
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907771
   j =  2                              :            46107
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-3
 p-value of test no 79                 :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.25
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.92
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.23
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.57
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.75
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.19
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.44
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.43
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.74
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.84
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.34
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.28
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.63
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.51
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.05
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.94
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.19
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.62
 p-value of test no 156                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.03
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.79
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.45
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  120.48
 p-value of test no 160                :  5.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.23
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.85
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  413.95
 p-value of test no 163                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.80
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.39
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.07
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.08
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.85
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.48
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.31
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.07
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.93
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5226.38
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.32
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.36
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   33.22
 p-value of test no 178                :  9.0e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    2.02
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.36
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.57
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.46
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.80
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.62
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.79
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4447.12
 p-value of test no 227                :  1.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.81
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.80
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.11
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.56
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999991916
 
 Normal statistic for number of bits   :  -0.064
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.80
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000002476
 
 Normal statistic for number of bits   :   0.020
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:36.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     5.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  81  LinearComp, r = 0               9.0e-4
  97  HammingIndep, L=300, r=0        1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98926599.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56637
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7108
 p-value of test no 20                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.28
 p-value of test no 22                 :  6.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.39
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 35                 :    0.9984
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.30
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.97
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.66
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.99
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.71
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.70
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.10
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.53
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.90
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.60
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.63
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.87
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.97
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.33
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.44
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.38
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.72
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907922
   j =  2                              :            46036
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908643
   j =  2                              :            45674
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.06
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.34
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.48
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.81
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.17
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.62
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.67
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.31
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.34
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.23
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.76
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17275.80
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.69
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.57
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.42
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.70
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.82
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.45
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.10
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.24
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.04
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.93
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.38
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.09
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.89
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.49
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.98
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.04
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.78
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.72
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.37
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.94
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.02
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.59
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.04
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.11
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.39
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.39
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.89
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.34
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.10
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.72
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.09
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.32
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.44
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.66
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.78
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.16
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.05
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.59
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.64
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.70
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999869870
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.56
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999960821
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:18.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99778567.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56638
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.32
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.92
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.77
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.53
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.33
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.54
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.53
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.81
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  377.10
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.17
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.64
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.30
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.95
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.96
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.47
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908232
   j =  2                              :            45881
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907667
   j =  2                              :            46162
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
 p-value of test no 104                :    0.9961
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.26
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.73
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.95
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.78
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.56
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.81
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.33
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.85
 p-value of test no 129                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.97
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.42
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17129.42
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.86
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.85
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.23
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.65
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.13
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.52
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.40
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.65
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.33
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.28
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.22
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.58
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.86
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.96
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.25
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.92
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.48
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.62
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.70
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.42
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.00
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.60
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.42
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.56
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.35
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.04
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.15
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.85
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.42
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 186                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.36
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.06
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.69
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.09
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.94
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.99
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.87
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.91
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.75
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.95
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.26
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.16
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000076150
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.23
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000117109
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:40.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100827143.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56639
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.62
 p-value of test no 23                 :  1.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    4.11
 p-value of test no 30                 :  7.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.82
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.53
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.43
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.53
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.42
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.94
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.80
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.23
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.14
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.02
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.86
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.50
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.80
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.75
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.79
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908686
   j =  2                              :            45654
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908269
   j =  2                              :            45861
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.72
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.45
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.96
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.01
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.62
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.72
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.95
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.70
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17168.32
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.27
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.93
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.40
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.78
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.81
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.65
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.72
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.23
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.94
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.89
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.44
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.85
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.05
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.13
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.93
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.80
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.99
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.55
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.08
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.73
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.01
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.97
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.04
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.34
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.90
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.02
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.28
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.68
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.49
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.81
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.45
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.56
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.48
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.65
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.63
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.01
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.59
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.01
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.56
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.77
 p-value of test no 231                :  5.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000007018
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.66
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999809927
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
 p-value of test no 245                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.66
 p-value of test no 248                :  3.9e-3
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:04.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101842951.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56640
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 12                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.27
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     835
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.26
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.41
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.32
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.89
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.64
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.51
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.05
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.39
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.73
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.65
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.78
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.03
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.46
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.93
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.70
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908431
   j =  2                              :            45780
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908536
   j =  2                              :            45726
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.89
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.97
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.37
 p-value of test no 121                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.60
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.48
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.67
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.82
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.20
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17402.62
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.35
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.82
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.00
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.79
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.43
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.72
 p-value of test no 152                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.47
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.59
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.24
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.92
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.65
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.01
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.67
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.09
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.87
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.96
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.72
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.31
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.48
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.85
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.07
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.95
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.54
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.01
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.55
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.08
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.02
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.22
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.23
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.30
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.66
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.45
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.68
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.44
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.05
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.53
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.58
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.14
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.83
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.39
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000093778
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.79
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999946922
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 245                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 248                :    0.9903
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:34.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82640918.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56641
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    4.38
 p-value of test no 26                 :  5.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.66
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.43
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.59
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.37
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.93
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.42
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.44
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.17
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.24
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.40
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.71
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.29
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.09
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.30
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.83
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.77
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908696
   j =  2                              :            45646
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908435
   j =  2                              :            45775
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.15
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.33
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.74
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.29
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.84
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.91
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.65
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.71
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17559.11
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.31
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.64
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.80
 p-value of test no 148                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.74
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.95
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.16
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.77
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.09
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.76
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.52
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.63
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.39
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.85
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.45
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.82
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.89
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.96
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.71
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.85
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.41
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.29
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.69
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.21
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.62
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.56
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.47
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.01
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.74
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.29
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.62
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.70
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.89
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.59
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.22
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.33
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.88
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.46
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.01e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.63
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.76
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.57
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.37
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.28
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.21
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999956459
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.32
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999790478
 
 Normal statistic for number of bits   :   -1.66
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.089
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:41.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83886102.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56642
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 3                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 4                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 10                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.87
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.84
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.23
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  184.27
 p-value of test no 54                 :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.37
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.37
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.17
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.11
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.93
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.14
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.20
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.54
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46294
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907419
   j =  2                              :            46280
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907926
   j =  2                              :            46025
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 86                 :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
 p-value of test no 94                 :    0.9949
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.12
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.14
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.36
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.42
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.66
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.07
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.49
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.37
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.81
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17384.14
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.01
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.06
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.13
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.22
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.24
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.74
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.38
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.83
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.86
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.58
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.01
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.90
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.36
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.57
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.26
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.82
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.73
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.16
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.66
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.20
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.07
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.17
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.25
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.66
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.72
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.38
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.89
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.07
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.96
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.33
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.02
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.21
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.00
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.76
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.43
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.25
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.78
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12097.27
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.32
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000032431
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.01
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999987083
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:13.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            0.9990 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84770838.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56643
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 8                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 14                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.75
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.99
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.75
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.17
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.54
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.67
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6846.95
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.64
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.11
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.66
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.55
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45703
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908599
   j =  2                              :            45693
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908652
   j =  2                              :            45668
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.79
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.39
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.10
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.05
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.67
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.60
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.93
 p-value of test no 125                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.41
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.05
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.02
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.85
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.42
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.49
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.16
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.23
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.56
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.77
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.97
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.46
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.38
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.59
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.52
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.01
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.80
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.52
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.56
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.47
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.69
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.36
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.82
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.32
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.58
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.94
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.08
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.43
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.59
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.32
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.83
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.54
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.58
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.40
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9961
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.07
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.25
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.59
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.06
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.14
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.73
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4294.79
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.49
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.81
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.87
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.85
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999948068
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.11
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000099154
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.44e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:45.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85688342.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56644
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.73
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.12
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.66
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.95
 p-value of test no 52                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.79
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.13
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.07
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.10
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.92
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.31
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.55
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.46
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908342
   j =  2                              :            45826
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907925
   j =  2                              :            46027
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.90
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.54
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.75
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.35
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.74
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.84
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.11
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.58
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.14
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.72
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.68
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.54
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.48
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.93
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   53.12
 p-value of test no 153                :  8.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.71
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.57
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.85
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.49
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.86
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.51
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.45
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.11
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.04
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.64
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.27
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.33
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.17
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.12
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.07
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.16
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.92
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.34
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.23
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.27
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.91
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.90
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.85
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.94
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.44
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.55
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.98
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.66
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.59
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.85
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.07
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.47
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.07
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999861047
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.10
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999901331
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9920
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.57
 p-value of test no 248                :  5.1e-3
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:09.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      8.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86605846.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56645
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.32
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.41
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.29
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.83
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.97
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.66
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.26
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.48
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.08
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.16
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.72
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.00
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.78
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908571
   j =  2                              :            45710
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46370
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870370
   j =  1                              :        399907264
   j =  2                              :            46362
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.14
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.70
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.81
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.87
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.65
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.52
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.83
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.63
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.77
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.11
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.38
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.75
 p-value of test no 147                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.56
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.92
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.31
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.91
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.91
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.84
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.00
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.78
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.62
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.98
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.99
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.89
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.63
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.58
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.63
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.82
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.56
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.89
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.80
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.50
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.12
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.33
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.35
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.60
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.98
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.67
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.65
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.12
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.20
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.26
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.83
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.91
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.42
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.96
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.80
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.60
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.07
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000086068
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.79
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000095446
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:29.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87588886.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56646
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 9                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.37
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.08
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.93
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.46
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.19
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.35
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.78
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.92
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.68
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.95
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.19
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.49
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.61
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.68
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908130
   j =  2                              :            45926
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908417
   j =  2                              :            45790
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.29
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.94
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.93
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.31
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.05
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.74
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.83
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.43
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.77
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.85
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.81
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.90
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17277.08
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.86
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.01
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.35
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.36
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.46
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.59
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.42
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.46
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.46
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.12
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.08
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.92
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.36
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.54
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.64
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.11
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.13
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.71
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.23
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.19
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.47
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.18
 p-value of test no 170                :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.79
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.19
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.29
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.97
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.59
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.71
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.56
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.27
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.75
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.76
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.53
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.32
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.24
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.60
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.86
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.49
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.93
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999834176
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.23
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000046942
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    2.02
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:29.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88571926.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56647
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.57
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.14
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.56
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.58
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.32
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.58
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.72
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.54
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.10
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6828.38
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.27
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.10
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.15
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.99
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908508
   j =  2                              :            45737
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908118
   j =  2                              :            45938
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.24
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.78
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.77
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.85
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.30
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.50
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 130                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 132                :  8.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.77
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.28
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.70
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.01
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.22
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.38
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.99
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.71
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.34
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.80
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.35
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.98
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.01
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.83
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.40
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.89
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.76
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.46
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.77
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.99
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.97
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.28
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.78
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.03
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.76
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.17
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.77
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.50
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.28
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.27
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.49
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.16
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.85
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.35
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.37
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.83
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.28
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.04
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.72
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.43
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12141.58
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11591.54
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.21
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000002989
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.86
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000048742
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:12.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89620502.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56648
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 12                 :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5563
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.37
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    4.49
 p-value of test no 32                 :  5.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.14
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.53
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.56
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.88
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.79
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.21
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.31
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.24
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.75
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.83
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.02
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.10
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.07
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908852
   j =  2                              :            45568
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908399
   j =  2                              :            45799
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 78                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.78
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.22
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.30
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.67
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.66
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 126                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.40
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.82
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.11
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.75
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.95
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.76
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.19
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.71
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.35
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.07
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.22
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.29
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.53
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.53
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.26
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.87
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.89
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.91
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.52
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.49
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.56
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.26
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.14
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.92
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.42
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.58
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.17
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.53
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.14
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.45
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.13
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.21
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.33
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.16
 p-value of test no 176                :  7.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.29
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.26
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.99
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9978
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.69
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.30
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.54
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.17
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.66
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.04
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.59
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.46
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.86
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.70
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.22
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000231856
 
 Normal statistic for number of bits   :    1.83
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.05
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999969050
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.090
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:22.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90701846.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56649
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.29
 p-value of test no 34                 :  7.7e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.18
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.24
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.55
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.04
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.64
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.23
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.82
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.22
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.91
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.36
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.61
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.28
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5230.77
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46338
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870338
   j =  1                              :        399907324
   j =  2                              :            46338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46047
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907909
   j =  2                              :            46041
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.33
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.81
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.69
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.77
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.71
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 126                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.65
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.20
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.19
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17248.88
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.13
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.44
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.57
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.40
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.55
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.57
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.70
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.91
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.29
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.95
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.90
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.18
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.23
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.18
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.09
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.50
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.19
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.64
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.36
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.01
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.28
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.39
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.11
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.25
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.65
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.02
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.87
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.06
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.93
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.42
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.79
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.60
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.25
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.09
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.59
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.43
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.90
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.97
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.04
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.78
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.96
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999999206
 
 Normal statistic for number of bits   : -6.28e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.73
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999868712
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.057
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:10.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            7.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92012566.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56650
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997383
   j =  2                              :             1307
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.85
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.58
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.72
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.70
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.43
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.20
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.85
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.10
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.05
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.47
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.10
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.15
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.27
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.84
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907744
   j =  2                              :            46119
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908493
   j =  2                              :            45743
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.42
 p-value of test no 85                 :  5.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.17
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.54
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.18
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.77
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.00
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.39
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.94
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17514.08
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.17
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.22
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.74
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.42
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.68
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.14
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.76
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.94
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.24
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.73
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.31
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.25
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.79
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.41
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.30
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.47
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.18
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.14
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.46
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.66
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.32
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.65
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.93
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.30
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.36
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.59
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.85
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.35
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.82
 p-value of test no 196                :  7.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.38
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.88
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.66
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.65
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 219                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.80
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.86
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.20
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.54
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.82
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.64
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.77
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999963950
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.69
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000141061
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.020
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 248                :    0.02
 
 Sample variance                       :    2.07
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:15.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93028374.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56651
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.16
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.89
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.69
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.61
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.18
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.29
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.11
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.06
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.08
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.79
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.36
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.23
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908175
   j =  2                              :            45911
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46096
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907814
   j =  2                              :            46084
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  4.9e-3
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.35
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.03
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.33
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.25
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.54
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.28
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.58
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.28
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.78
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-4
 p-value of test no 138                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.95
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17491.01
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.31
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.61
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.39
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.02
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.10
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.04
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.54
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.57
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.54
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.13
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.41
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.51
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.04
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.83
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.14
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.79
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.29
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.16
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.71
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.36
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.54
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.64
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.44
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.28
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.12
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.52
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.52
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.43
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.44
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.11
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.26
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10261.22
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 218                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 220                :    0.9928
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 221                :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4611.82
 p-value of test no 222                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.45
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.67
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.51
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.26
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.47
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.92
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999981563
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000095239
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 235                :  5.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 253                :    0.94
 
 Sample variance                       :    2.87
 p-value of test no 254                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:33.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94044182.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56652
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7108
 p-value of test no 20                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.68
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.73
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.82
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.76
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.45
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.72
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.23
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.75
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.81
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.27
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6904.36
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.63
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.29
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.16
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.43
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4918.51
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45330
 p-value of test no 70                 :    0.9949
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869330
   j =  1                              :        399909343
   j =  2                              :            45324
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908007
   j =  2                              :            45989
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.16
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.18
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.05
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.87
 p-value of test no 125                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.75
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.02
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.67
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.36
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 142                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17718.04
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.22
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.90
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.54
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.99
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.13
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.24
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.36
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.81
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.87
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.17
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.43
 p-value of test no 162                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.38
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.00
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.41
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.86
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.95
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.11
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.37
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.82
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.40
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.29
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.18
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.18
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.91
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.05
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.66
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.12
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.16
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.40
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.77
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.37
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.23
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.47
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.93
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.00
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12216.63
 p-value of test no 230                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.64
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000034990
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.86
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999842156
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 242                :    0.9989
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:26.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95027222.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56653
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 9                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4160
 p-value of test no 14                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.05
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.77
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.96
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.61
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.58
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.14
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.90
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.19
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.95
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.09
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.72
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.76
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.42
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.48
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.71
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5206.99
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908260
   j =  2                              :            45864
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907854
   j =  2                              :            46067
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.52
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.73
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.57
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.98
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.61
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.76
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.95
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.12
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.31
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17070.40
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.34
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.56
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.85
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.87
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.34
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.40
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.25
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.19
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.14
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.57
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.42
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.38
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.32
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.47
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.41
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.27
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.98
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.64
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.11
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.36
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.66
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.20
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.90
 p-value of test no 172                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.84
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.85
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.45
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.47
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9927
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.14
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.71
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.35
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.55
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.90
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.32
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.38
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 224                :    0.9922
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4688.61
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.43
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.33
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.07
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.27
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.53
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000145936
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.52
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999972977
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:27.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96010262.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56654
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.09
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.33
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.87
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.76
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.22
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.20
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.23
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1546.78
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7219.92
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.45
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.00
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.95
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.62
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.93
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908830
   j =  2                              :            45579
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907822
   j =  2                              :            46089
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  7.0e-3
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 81                 :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  4.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.19
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.16
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.93
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.56
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.05
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.93
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.60
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.98
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.81
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.79
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.83
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.96
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.52
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.98
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.16
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.76
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.81
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.43
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.48
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.99
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.71
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.86
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.80
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.11
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.06
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.17
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.57
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.46
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.07
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.61
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.19
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.52
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.97
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.77
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.49
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.01
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.47
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.87
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.16
 p-value of test no 189                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.11
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.45
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.51
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.73
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.74
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.01
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.60
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.23
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.46
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12118.16
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.49
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.32
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000000796
 
 Normal statistic for number of bits   : 6.29e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.12
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999902948
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:55.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97026070.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56655
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    3.41
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.80
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.60
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.48
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.90
 p-value of test no 50                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.83
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.87
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.07
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.47
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.31
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.00
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.90
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.76
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.34
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.65
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908339
   j =  2                              :            45826
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907777
   j =  2                              :            46107
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.78
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.55
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.90
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.20
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.39
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.04
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.63
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.22
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.99
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.08
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.84
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.01
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.40
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.05
 p-value of test no 152                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.35
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.06
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.15
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.23
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.86
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.80
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.29
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.15
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.02
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.07
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.49
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.71
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.85
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.89
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.00
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.63
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.75
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.85
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.50
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.86
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.00
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.65
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.62
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.01
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.22
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.24
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.89
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.30
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.05
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.06
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.36
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.38
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.35
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.89
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.46
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999924350
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.90
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000150124
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.015
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.98
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-3
 p-value of test no 250                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 251                :  6.5e-5    *****
 
 Anderson-Darling statistic = A2       :    5.95
 p-value of test no 252                :  1.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.13
 p-value of test no 253                :  8.8e-4    *****
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:45.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  106  AutoCor, d=3, r=27              8.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98074646.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56656
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.03
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.59
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.40
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.04
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.14
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.54
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.92
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.46
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.88
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.49
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.10
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.51
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.76
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5242.01
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908309
   j =  2                              :            45841
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908457
   j =  2                              :            45761
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.65
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.30
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.72
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.34
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.79
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.91
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.60
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.40
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.47
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.83
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.15
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.55
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.29
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.86
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.53
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.00
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.18
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.28
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.15
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.80
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.31
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.39
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.81
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.96
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.27
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.37
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.22
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.09
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.79
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4739.38
 p-value of test no 168                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.98
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.63
 p-value of test no 170                :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.14
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.91
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.01
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.01
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.18
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.65
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.64
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.84
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.83
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.84
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.77
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.44
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5111.19
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.44
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.18
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.90
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.21
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.60
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000032491
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.48
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999892691
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:33.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98992150.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56657
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 5                  :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.19
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.21
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.22
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.58
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.63
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.98
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.78
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.17
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  163.03
 p-value of test no 67                 :  4.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.05
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908238
   j =  2                              :            45872
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.79
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.83
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.12
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.37
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.37
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.39
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.30
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.58
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.21
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.05
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.48
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17706.86
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.95
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.58
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.77
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.82
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.72
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.81
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.88
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.14
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.46
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.43
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.88
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.61
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.44
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.03
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.39
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.82
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.90
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.72
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.92
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.17
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.95
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.93
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.64
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.88
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.95
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.21
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.70
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.95
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.92
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.52
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.18
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.52
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.31
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.40
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.28
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10318.45
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.80
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.65
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.61
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.08
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.03
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.51
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   24.66
 p-value of test no 231                :    0.9998    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999857507
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.06
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999796709
 
 Normal statistic for number of bits   :   -1.61
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:41.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  101  Run of bits, r = 0              0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99975190.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56658
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1514
 p-value of test no 9                  :  3.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334634
   j =  1                              :        599996972
   j =  2                              :             1514
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    4.29
 p-value of test no 26                 :  6.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.05
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.25
 p-value of test no 28                 :  6.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.84
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.96
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.79
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.79
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.20
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.56
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.99
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.07
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.41
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.86
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.82
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.04
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5247.42
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908133
   j =  2                              :            45929
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46108
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907787
   j =  2                              :            46102
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.92
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.53
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.66
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.03
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.33
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.23
 p-value of test no 124                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.42
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.68
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.93
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.36
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.53
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17197.84
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.72
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.24
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.16
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.44
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.01
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.24
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.21
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.40
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.16
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.62
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.40
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.69
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.87
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.54
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.44
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.46
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.65
 p-value of test no 167                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.55
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.11
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.96
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.34
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.60
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.44
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.64
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.38
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.67
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.70
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.43
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.98
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.14
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.16
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9738.11
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.68
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.01
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.38
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.91
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12087.19
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.03
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.56
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999951704
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.34
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999910379
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:10.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           3.5e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100990998.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56659
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 8                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.49
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.47
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.01
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.57
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.76
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.91
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.34
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.36
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.64
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.42
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.10
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908161
   j =  2                              :            45918
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908547
   j =  2                              :            45722
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.18
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.80
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.32
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.75
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.99
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.60
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.30
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.87
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
 p-value of test no 138                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  170.88
 p-value of test no 141                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.45
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.54
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.27
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.90
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.31
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.99
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.43
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.31
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.44
 p-value of test no 153                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.37
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.28
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.95
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.47
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.27
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.48
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.97
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.99
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.95
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.35
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.99
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.83
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.50
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.06
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.06
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.98
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.98
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.19
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.57
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.24
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.08
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.16
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.94
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.09
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.83
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.88
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10274.66
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.49e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.36
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.48
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.70
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.59
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.73
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12168.06
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.22
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999996206
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.18
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999985619
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:52.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102006805.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56660
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 9                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    3.53
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.10
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.41
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.13
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.15
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.92
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1326.94
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7335.53
 p-value of test no 57                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.57
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.10
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.86
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.18
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908406
   j =  2                              :            45794
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908270
   j =  2                              :            45856
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 74                 :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.39
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.84
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.11
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.03
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.80
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.46
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.45
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.12
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17308.87
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.61
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.69
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.27
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.03
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.90
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.27
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.87
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.68
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.01
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.73
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.75
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.69
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.03
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.76
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.70
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.83
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.18
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.76
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.97
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.80
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.78
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.44
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.27
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.15
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.62
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.61
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.67
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.64
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.76
 p-value of test no 175                :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.95
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.07
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.99
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.22
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.64
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.57
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.30
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.46
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.84
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.34
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.42
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.47
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.41
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999876158
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.83
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000039163
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 248                :  4.6e-3
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:41.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82673687.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56661
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.41
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.52
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.09
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.25
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.07
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.82
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.10
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.95
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.92
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.23
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.90
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907772
   j =  2                              :            46105
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908141
   j =  2                              :            45925
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
 p-value of test no 86                 : 1 -  9.4e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
 p-value of test no 90                 :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.21
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.24
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.48
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.75
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.98
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.41
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.16
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.69
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.52
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.56
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.17
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.15
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.96
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.10
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.63
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.00
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.26
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.70
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.23
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.73
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.25
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.33
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.47
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.66
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.23
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.30
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.22
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.42
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.36
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.00
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.56
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.87
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.83
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.14
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.10
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.58
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.96
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.86
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.91
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.51
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.00
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.73
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.05
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.78
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.00
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.37
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.13
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.16
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.08
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000082240
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999897890
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.035
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:14.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83689495.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56662
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    3.45
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    5.30
 p-value of test no 45                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.03
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.74
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.43
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.98
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.20
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.15
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.46
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.69
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.42
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.75
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908649
   j =  2                              :            45668
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45473
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869473
   j =  1                              :        399909056
   j =  2                              :            45469
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.01
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.36
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.23
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.65
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.48
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.71
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.53
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.55
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17426.14
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.38
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.88
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.55
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.96
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.33
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.04
 p-value of test no 153                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.01
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.00
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.05
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.47
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.90
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.55
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.65
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.02
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.72
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.81
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.93
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.43
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.28
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.94
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.64
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.67
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.10
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.19
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.58
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.24
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.98
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.28
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.05
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.81
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.71
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.37
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.05
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4719.06
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5079.85
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.49
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.28
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.99
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.19
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.11
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999890972
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.96
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000074851
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:23.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84705303.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56663
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997251
   j =  2                              :             1373
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7524
 p-value of test no 18                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9949
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.73
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.20
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.62
 p-value of test no 51                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.06
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.64
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.80
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.46
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.95
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.65
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.87
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.82
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.10
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908088
   j =  2                              :            45947
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.48
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.00
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.21
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.25
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.60
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.34
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.77
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.06
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.97
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.52
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.38
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.36
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.38
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.16
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.29
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.07
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.60
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.87
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.56
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.40
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.83
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.42
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.66
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.12
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.70
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.57
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.07
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.54
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.28
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.78
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.23
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.94
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  305.96
 p-value of test no 171                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.43
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.86
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.84
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.13
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.84
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.47
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.56
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.78
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-3
 p-value of test no 212                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 213                :  6.2e-4    *****
 
 Anderson-Darling statistic = A2       :    7.46
 p-value of test no 214                :  2.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10554.86
 p-value of test no 215                :  5.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.82
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.36
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.06
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.39
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.83
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.05
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.73
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999962558
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.16
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999848642
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.83
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:17.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  91  HammingWeight2, r = 27          5.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85622807.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56664
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 5                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.67
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.65
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.17
 p-value of test no 47                 :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.24
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.86
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.59
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.68
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.64
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.68
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.27
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.31
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.55
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.27
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.39
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.62
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.36
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.19
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908332
   j =  2                              :            45828
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907948
   j =  2                              :            46023
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.11
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.41
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.17
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.48
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.81
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.05
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.80
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.45
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.84
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.37
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.64
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.40
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.27
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.42
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.93
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.91
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.30
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.14
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.58
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.43
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.02
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.35
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.90
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.14
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.70
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.56
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.78
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.43
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.96
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.75
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.14
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.75
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.00
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.71
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.81
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.08
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.75
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.53
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.35
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.68
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.66
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.45
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.24
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.67
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10256.82
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.11
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 223                :  7.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 225                :  9.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4676.98
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.15
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.30
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.08
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.79
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.74
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999954563
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.81
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999929435
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:12.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86638615.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56665
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.58
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.37
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.17
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.85
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.97
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.22
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.75
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.14
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.04
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.13
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.03
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.36
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4882.26
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908844
   j =  2                              :            45569
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907687
   j =  2                              :            46152
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.97
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.68
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.40
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   15.60
 p-value of test no 122                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.83
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.81
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   53.03
 p-value of test no 125                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.61
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.23
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17163.54
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.62
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.33
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.71
 p-value of test no 148                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.27
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.43
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.15
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.68
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.68
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.98
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.42
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.29
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.81
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.73
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.06
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.83
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.81
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.46
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.20
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.39
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.05
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.35
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.70
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.05
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.45
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.35
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.66
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.75
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.17
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.25
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.55
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.80
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.68
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.68
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.03
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.78
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.89
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.84
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.06
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.27
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.79
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.05
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.33
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.70
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.10
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000056185
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.52
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000114811
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9949
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87621655.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56666
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     530
 p-value of test no 31                 :    0.9981
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.07
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.36
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.76
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.63
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.51
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.77
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.79
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.52
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.62
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.71
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.72
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.16
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.64
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908299
   j =  2                              :            45837
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907924
   j =  2                              :            46029
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.29
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.39
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.47
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.24
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.41
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.34
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.70
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.35
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.51
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.11
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.30
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.64
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.39
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.01
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.50
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.81
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.82
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.01
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.43
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.16
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.23
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.58
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.92
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.73
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.06
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.46
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.22
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.63
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.20
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.15
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.26
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.74
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.45
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5237.09
 p-value of test no 173                :  9.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.21
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.69
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.46
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-4
 p-value of test no 185                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.49
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.53
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.80
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.77
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.62
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.43
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4662.50
 p-value of test no 226                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.48
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.93
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.33
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.59
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.43
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999895067
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.03
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000122074
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.097
 p-value of test no 248                :    0.54
 
 Sample variance                       :    2.17
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.061
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88539159.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56667
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 17                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7105
 p-value of test no 18                 :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.44
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.28
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.72
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.31
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.57
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7255.02
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.05
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.79
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.96
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4928.88
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908137
   j =  2                              :            45927
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908230
   j =  2                              :            45879
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-4
 p-value of test no 112                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 114                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.48
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.04
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.50
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.28
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.64
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.93
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.96
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.44
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.25
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.66
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.27
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.68
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.67
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.60
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.27
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.21
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.42
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.16
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.94
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.87
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.98
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.83
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.06
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.88
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.30
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.07
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.38
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.92
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.56
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.25
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.17
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.97
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.95
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.04
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.85
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.98
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.24
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.52
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.88
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.33
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.72
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.24
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.49
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.90
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.74
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.66
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.12
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.57
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.70
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000027616
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.71
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999917129
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:48.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89587735.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56668
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5220
 p-value of test no 13                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.57
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.51
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.08
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.97
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.33
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.11
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.36
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.47
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.32
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.06
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.78
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.58
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46261
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870261
   j =  1                              :        399907485
   j =  2                              :            46247
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-4
 p-value of test no 113                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 114                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.51
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.43
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.63
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.87
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.61
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.96
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.65
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.044
 p-value of test no 135                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.23
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.32
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.71
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.39
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.59
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.41
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.62
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.61
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.19
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.73
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.53
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.40
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.90
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.71
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.35
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.08
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.16
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.09
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.73
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.59
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.95
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.16
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.95
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.48
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.97
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.40
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.64
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.91
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.94
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.43
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.09
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.64
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.27
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.61
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.40
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.73
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 217                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
 p-value of test no 220                :    0.9977
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4625.21
 p-value of test no 222                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.53
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.79
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.89
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.17
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.46
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.23
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000038929
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.10
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999985094
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:12.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90570775.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56669
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 8                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.02
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.86
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.68
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.93
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.84
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.53
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.17
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.83
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.34
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.71
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.80
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.25
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.01
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907938
   j =  2                              :            46031
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908239
   j =  2                              :            45876
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.01
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.13
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.83
 p-value of test no 122                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.77
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.95
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.31
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.23
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.94
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.38
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17273.63
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.71
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.48
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.82
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.67
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.65
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.92
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.41
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.81
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.24
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.59
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.87
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.82
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.29
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.09
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.97
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.51
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.77
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.75
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.07
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.04
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.36
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.85
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.42
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.80
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.21
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.25
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.84
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.52
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.86
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.67
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  261.83
 p-value of test no 203                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.46
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.65
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.98
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.22
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.39
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.32
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.34
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.83
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.83
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.68
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999885446
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.87
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999981743
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:24.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91488279.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56670
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    3.61
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.41
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.09
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.02
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.64
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.29
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.42
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.20
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.78
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.94
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.90
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.20
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.64
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.71
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.69
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908372
   j =  2                              :            45811
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907774
   j =  2                              :            46104
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.65
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.10
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.64
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.84
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.88
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.44
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.21
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.34
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.93
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.99
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.65
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.07
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.43
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.18
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.84
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.89
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.96
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.27
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.15
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.41
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.61
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.19
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.98
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.77
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.61
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.12
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.16
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.30
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.15
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.49
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.71
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.25
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.84
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.59
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.89
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.58
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.15
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.31
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.56
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.65
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 200                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.53
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.70
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.32
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.91
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.05
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.39
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.56
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.36
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.81
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.56
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.80
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999900476
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.68
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000094681
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:58.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92504087.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56671
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.90
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.03
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.61
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.01
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.63
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.06
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.75
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.58
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.65
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.63
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.53
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907665
   j =  2                              :            46160
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46408
 p-value of test no 71                 :  6.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870408
   j =  1                              :        399907189
   j =  2                              :            46398
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.01
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.81
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.40
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.35
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.85
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.69
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.69
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.71
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.88
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.25
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.54
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.20
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.83
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.60
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.69
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.28
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.64
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.66
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.51
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.81
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.38
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.78
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.43
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.53
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.40
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.95
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5276.09
 p-value of test no 168                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.19
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.44
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.71
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.63
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5267.34
 p-value of test no 173                :  4.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.01
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.02
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.28
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.69
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.68
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.17
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.95
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.55
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.53
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.84
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.45
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.86
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.44
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.14
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.81
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.10
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999977285
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.56
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999952799
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:33.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93487127.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56672
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.66
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.54
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.73
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.49
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.37
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.37
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.37
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.23
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.93
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 62                 :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.81
 p-value of test no 65                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.51
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.23
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907711
   j =  2                              :            46140
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908239
   j =  2                              :            45873
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.11
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.45
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.09
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.22
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.50
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.07
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.01
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.59
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.13
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.62
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17155.82
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.01
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.07
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.11
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.73
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.75
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.51
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.09
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.88
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.27
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.68
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.05
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.89
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.40
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.69
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.86
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.22
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.89
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.91
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.45
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.70
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.86
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.48
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.98
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.77
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.94
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.26
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.09
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 181                :  8.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 182                :  8.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.45
 p-value of test no 183                :  7.1e-3
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.57
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.57
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.92
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.26
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.17
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.50
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.60
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.71
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.83
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.16
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.11
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999992555
 
 Normal statistic for number of bits   :  -0.059
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.27
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999968321
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.023
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:26.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94502935.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56673
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.00
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.09
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.50
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.57
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.02
 p-value of test no 53                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.77
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.41
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.91
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6805.75
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.82
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.48
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.50
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.92
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907878
   j =  2                              :            46058
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908515
   j =  2                              :            45738
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.22
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.70
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.15
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.17
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.11
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.96
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.60
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.63
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.49
 p-value of test no 136                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.49
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17595.77
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.59
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.55
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.56
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.18
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.62
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.55
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.15
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.20
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.14
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.95
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.77
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.86
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.90
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.87
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.40
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.74
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.47
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.37
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.03
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.72
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.17
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.57
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.38
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.79
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.32
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.47
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.27
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.33
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.11
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.06
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.82
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.39
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.31
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.01
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.68
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.76
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.82
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.53
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.42
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.85
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999967478
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.10
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000076576
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:59.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95518743.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56674
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    4.60
 p-value of test no 32                 :  4.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9916
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.79
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.54
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.49
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.44
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.13
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.18
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.58
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.29
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.04
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.42
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.25
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.93
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.28
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.17
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  161.06
 p-value of test no 67                 :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.20
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908024
   j =  2                              :            45985
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907892
   j =  2                              :            46045
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 77                 :    0.9936
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.53
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.53
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.42
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.99
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.18
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.86
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.65
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.17
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.52
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.70
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.42
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.23
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.80
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.62
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.47
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.16
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.07
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.68
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.84
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.44
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.07
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.48
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.45
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.51
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.71
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.60
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.95
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.27
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.15
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.78
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.97
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.09
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.41
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.06
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.26
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.00
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.36
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.84
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.14
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.16
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.19
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.92
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.23
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.85
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.59
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.18
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.17
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.65
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.29
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.39
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.82
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999996146
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.08
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999843728
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.053
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:32.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96501783.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56675
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.97
 p-value of test no 22                 :  1.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.67
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.56
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.85
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.22
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.81
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.31
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.31
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.13
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.30
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.13
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.36
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.38
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.71
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.04
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.18
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907686
   j =  2                              :            46154
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908344
   j =  2                              :            45822
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.81
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.96
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.74
 p-value of test no 121                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.11
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.67
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.04
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.89
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.82
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.33
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.13
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.02
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.73
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.23
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.46
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.16
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.70
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.09
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.50
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.63
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.55
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.19
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.16
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.53
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.24
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.30
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.11
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.38
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.29
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.20
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.17
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.41
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.47
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.99
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  149.52
 p-value of test no 170                :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.25
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.99
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.90
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.09
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.81
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.91
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.22
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.96
 p-value of test no 198                :  7.3e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.49
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.06
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.33
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.96
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 221                :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.43
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.37
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.15
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.24
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.00
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.21
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.39
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000090145
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999864638
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 251                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    4.83
 p-value of test no 252                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.78
 p-value of test no 253                :  2.7e-3
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:21.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97714199.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56676
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7098
 p-value of test no 21                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    3.12
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.56
 p-value of test no 34                 :  5.8e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.05
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.72
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.38
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.61
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.22
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.05
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6894.99
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.76
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.24
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.14
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.50
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.73
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908023
   j =  2                              :            45984
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 73                 :    0.9904
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 99                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.45
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.23
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.34
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.67
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.45
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.06
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.43
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.07
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.29
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.27
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.14
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.54
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.23
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.39
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.12
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.36
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.40
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.42
 p-value of test no 156                :    0.9929
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.48
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.68
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.82
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.69
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.60
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.36
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.51
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.18
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.98
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.65
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.11
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.71
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.14
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.25
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.94
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.08
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.69
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.61
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.16
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.57
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.13
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.59
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.96
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.40
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.34
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.65
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.75
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.30
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.02
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.25
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.39
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.68
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000007624
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.37
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000186295
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.091
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:01.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            5.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98959383.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56677
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5264
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7141
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.04
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.64
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.85
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.46
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.28
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.03
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.79
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.17
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.60
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.19
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.58
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.81
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.43
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.65
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.05
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.62
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908019
   j =  2                              :            45980
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908316
   j =  2                              :            45839
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.65
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.67
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.55
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.01
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.30
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.78
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.13
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.88
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.91
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.84
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.93
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.92
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.19
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.27
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.10
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.78
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.84
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.80
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.36
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.38
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.55
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.70
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.89
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.94
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.60
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.66
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.60
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.72
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.49
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.07
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.34
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.04
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.80
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.22
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.64
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.72
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.14
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.85
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.89
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.56
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.54
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.29
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.52
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.26
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.50
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.20
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.32
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.34
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.90
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.37
 p-value of test no 231                :    0.9941
 
 
 -----------------------------------------------
 Total number of bits:  8000074506
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.15
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999984347
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    2.71
 p-value of test no 239                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:57.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99942423.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56678
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.47
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.59
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.17
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.83
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.71
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.72
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.89
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.81
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.62
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.62
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.01
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.38
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.35
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.93
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907989
   j =  2                              :            45995
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907852
   j =  2                              :            46065
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.66
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.44
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.53
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.30
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
 p-value of test no 126                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.35
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.91
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9900
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.19
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17159.58
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.47
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.65
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.57
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.72
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.64
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.78
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.46
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.48
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.73
 p-value of test no 155                :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.33
 p-value of test no 156                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.48
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.74
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.88
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.65
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.59
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.03
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.63
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.40
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.52
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.64
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.25
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.48
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.21
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.71
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.69
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.27
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.26
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.91
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.92
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.45
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.86
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.97
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.68
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.41
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.65
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.95
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.63
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.49
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.22
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.72
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.86
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.81
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000050662
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.04
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000020845
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.021
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:01.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100958231.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56679
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.55
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.02
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.50
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.75
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.77
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.96
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.21
 p-value of test no 53                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.09
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.17
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.89
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.51
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.23
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-3
 p-value of test no 63                 :    0.9987
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   36.81
 p-value of test no 65                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.62
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.54
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.72
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908407
   j =  2                              :            45795
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46185
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907634
   j =  2                              :            46177
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.90
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.37
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.27
 p-value of test no 121                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.44
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.30
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.06
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.55
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 130                :  5.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 132                :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.24
 p-value of test no 133                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.50
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.72
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17160.09
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.88
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.32
 p-value of test no 150                :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.02
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.13
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.19
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.96
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.01
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.63
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.09
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.58
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.17
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.91
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.40
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.08
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.13
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.94
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.95
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.88
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.68
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.43
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.03
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.80
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.85
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.03
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.47
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.85
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.68
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.26
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.36
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.34
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10202.70
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.53
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.57
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.52
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.24
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.96
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.53
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.94
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.77
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999962465
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.36
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999972593
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:41.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102072343.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56680
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.19
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.00
 p-value of test no 50                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.12
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.15
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.88
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.52
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.43
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.20
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.91
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.97
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.11
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.15
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.05
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.54
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908154
   j =  2                              :            45920
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907761
   j =  2                              :            46115
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-4
 p-value of test no 113                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 114                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.63
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.22
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.59
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.21
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.20
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.60
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.56
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.16
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.51
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.31
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.70
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.61
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.37
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.27
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.72
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.83
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.42
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.33
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.81
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.07
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.63
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.93
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.27
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.25
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.21
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.51
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.12
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.20
 p-value of test no 164                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.16
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.08
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.49
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.81
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.14
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.07
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.90
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.93
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5218.34
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.85
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.36
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.19
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.11
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.68
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.24
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9759.16
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.29
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.97
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.28
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.70
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.60
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.98
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.39
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.56
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999992120
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.71
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000004552
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:09.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82706456.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56681
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.9901
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.28
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.90
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.65
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.68
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.97
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.18
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.85
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.80
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.74
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.38
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 64                 :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.79
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.55
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.13
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.66
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908094
   j =  2                              :            45950
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908000
   j =  2                              :            45997
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 116                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.35
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.68
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.38
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.42
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.39
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.40
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.76
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.87
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.46
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-4
 p-value of test no 142                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 144                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18024.03
 p-value of test no 145                :  8.2e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.89
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.13
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.23
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.84
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.85
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.41
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.09
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.70
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.43
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.15
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.29
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.69
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.72
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.56
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.62
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.63
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.13
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.33
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.93
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.99
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.34
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.00
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.95
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.37
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.84
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.78
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.39
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.03
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.74
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.07
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.48
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.92
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.56
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.96
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 224                : 1 -  8.4e-5    *****
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4616.03
 p-value of test no 226                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.76
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.91
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.04
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.61
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000139339
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.25
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999941126
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:26.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  73  GCD                             8.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83492888.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56682
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.40
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.44
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.36
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.63
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.21
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.95
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.59
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.43
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.02
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.38
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908087
   j =  2                              :            45949
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907969
   j =  2                              :            46011
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
 p-value of test no 97                 :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.17
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.21
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.38
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.52
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.79
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.50
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.11
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.13
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.63
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.42
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17069.98
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.01
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.23
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.22
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.67
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.62
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.71
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.93
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.97
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.64
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.28
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.46
 p-value of test no 160                :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.68
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.20
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.49
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.92
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.69
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.36
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.27
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.53
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.89
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.29
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.00
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.11
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.66
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.07
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.59
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.53
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.15
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.36
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.99
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.69
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.06
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.12
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.98
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4392.01
 p-value of test no 227                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.03
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.65
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.05
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.53
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999924143
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.78
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999853559
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:42.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84443160.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56683
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9934
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.17
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.19
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.78
 p-value of test no 50                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.01
 p-value of test no 51                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.06
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.40
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.85
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.52
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.81
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.27
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.66
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4840.90
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908187
   j =  2                              :            45902
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908460
   j =  2                              :            45764
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.61
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.52
 p-value of test no 120                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.32
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.72
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.56
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.30
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.05
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.31
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.16
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.35
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.36
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.08
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.44
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.17
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.28
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.82
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.66
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.55
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.30
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.29
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.87
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.30
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.14
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.75
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.96
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.79
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.54
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.55
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.45
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.43
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.98
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  147.66
 p-value of test no 170                :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.17
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.40
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.47
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.00
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.50
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.60
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.77
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.44
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.33
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.19
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.64
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.61
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5044.54
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 224                :    0.9933
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.88
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.60
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.22
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.57
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.88
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.86
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000132244
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.12
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000011953
 
 Normal statistic for number of bits   :   0.094
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    2.48
 p-value of test no 244                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:38.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85196824.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56684
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.89
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.55
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.65
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.13
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.56
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.00
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.86
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.44
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.54
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.91
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 62                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 64                 :  5.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.64
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.89
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.06
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46339
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870339
   j =  1                              :        399907323
   j =  2                              :            46337
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908328
   j =  2                              :            45830
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 74                 :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9941
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.39
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.06
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.38
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.12
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.15
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 130                :  9.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    7.56
 p-value of test no 132                :  2.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   15.93
 p-value of test no 133                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.98
 p-value of test no 136                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 139                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.27
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17353.41
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.46
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.11
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.70
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.96
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.97
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.13
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.76
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.00
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.81
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.78
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.07
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.29
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.68
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.63
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.77
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.65
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.35
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.66
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.65
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.44
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.28
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.36
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.01
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.30
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.95
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.00
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.04
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.08
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.70
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.75
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.07
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.18
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9746.92
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.56
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.58
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.73
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.26
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.91
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.43
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.17
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999998879
 
 Normal statistic for number of bits   : -8.86e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.35
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000020068
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:02.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86212632.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56685
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.59
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.71
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.80
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.61
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.09
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.54
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.63
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.37
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.84
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.51
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.01
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.46
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.23
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.39
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.08
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.21
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5270.95
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908453
   j =  2                              :            45769
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908826
   j =  2                              :            45581
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.30
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.36
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.41
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.78
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.31
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 126                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.09
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.94
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.17
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.66
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.12
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.72
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.75
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.80
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.27
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.58
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.71
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.72
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.14
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.46
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.66
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.73
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.96
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.62
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.90
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.28
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.81
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.20
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.80
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.18
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.65
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.44
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.16
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.80
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.51
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.65
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.65
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.49
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 186                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.95
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.31
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.88
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.96
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.96
 p-value of test no 218                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.07
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4732.66
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.13
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.97
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.81
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.90
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.34
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000022831
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.95
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000081976
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:40.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87195672.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56686
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.02
 p-value of test no 40                 :  9.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.33
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.49
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.75
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.97
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.89
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.50
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.27
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.88
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.10
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.89
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.14
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.46
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908324
   j =  2                              :            45832
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908420
   j =  2                              :            45781
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.82
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.44
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.26
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.34
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.66
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.87
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.91
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.75
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.15
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.11
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.15
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.18
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.96
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.21
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.50
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.68
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.77
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.53
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.50
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.89
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.05
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.91
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.38
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.49
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.53
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.71
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.54
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.67
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.39
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.41
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.61
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.31
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.86
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.91
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.33
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.78
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.57
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.56
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.23
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.59
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9679.62
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
 p-value of test no 220                :    0.9978
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.64
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.77
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.35
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.74
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.35
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.95
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.60
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999949112
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.08
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999900383
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 236                :  1.2e-3
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 237                :  5.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.73
 p-value of test no 238                :  3.1e-3
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:58.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88375301.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56687
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 9                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.80
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.82
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.42
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.52
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.79
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.36
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.26
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.65
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.90
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1324.59
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.46
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.90
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.12
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.42
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.58
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908439
   j =  2                              :            45773
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  4.5e-3
 
 Anderson-Darling statistic = A2       :    6.42
 p-value of test no 81                 :  6.5e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  1.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
 p-value of test no 103                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.83
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.36
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.10
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.14
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.76
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.96
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.76
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.28
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.61
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.35
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.30
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.16
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.27
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.36
 p-value of test no 150                :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.38
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.64
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.09
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.81
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.37
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.85
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.83
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.55
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.15
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.07
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.62
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.09
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.03
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.71
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.94
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.52
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.41
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.46
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.19
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.20
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.40
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.24
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.50
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.47
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.43
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.22
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.14
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.84
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.32
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.15
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.19
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.09
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.41
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4313.92
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.89
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.61
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.68
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.66
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999887237
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.56
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999855257
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:24.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89227269.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56688
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4490
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.10
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.18
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.31
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.07
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.27
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.60
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.04
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.26
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.04
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.12
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.63
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.67
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.87
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.57
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4894.68
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908110
   j =  2                              :            45945
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908454
   j =  2                              :            45770
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.49
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.36
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.62
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.14
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.29
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.79
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.35
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.25
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.13
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17144.50
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.87
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.40
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.13
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.19
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.11
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.94
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.91
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.72
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.44
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.87
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.93
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.49
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.98
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.07
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.26
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.11
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.76
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.35
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.06
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.89
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.03
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.96
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.68
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.32
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.18
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.06
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.59
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.64
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.75
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.14
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.06
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.34
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4340.13
 p-value of test no 227                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.08
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.72
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.96
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.71
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000019636
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   90.81
 p-value of test no 233                :  1.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999910427
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:03.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90243077.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56689
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997225
   j =  2                              :             1386
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 8                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.44
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.15
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.73
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.73
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.03
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.35
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.14
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.30
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.37
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.34
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.69
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.30
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.50
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908185
   j =  2                              :            45906
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907870
   j =  2                              :            46062
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 93                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 106                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 2.76e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.91
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.04
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.29
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.43
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.58
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.52
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.80
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.76
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.11
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.73
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.23
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.44
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.83
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.75
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.29
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.11
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.55
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.47
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.76
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.26
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.91
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.97
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.66
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.68
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.59
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.30
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.63
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.44
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.10
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.49
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.09
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.18
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.28
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.86
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.61
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.88
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.01
 p-value of test no 176                :  2.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.61
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.28
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.90
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.56
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.13
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.60
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.20
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.80
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.17
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.56
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.89
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.59
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.84
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999903698
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.80
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999976022
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    2.23
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:20.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91258885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56690
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.59
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.11
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.04
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.44
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.57
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.78
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.50
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.27
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.20
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.30
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.17
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.77
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.35
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.43
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907928
   j =  2                              :            46030
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907955
   j =  2                              :            46016
   j =  3                              :                3
   j =  4                              :                1
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 97                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 98                 :    0.9931
 
 Anderson-Darling statistic = A2       :    6.35
 p-value of test no 99                 :  7.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 101                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 103                :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 105                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.10
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.79
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.59
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.85
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.14
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.13
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.79
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.51
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17374.16
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.05
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.10
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.44
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.95
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.88
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.70
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.02
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.26
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.80
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.93
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.34
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.44
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.29
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.82
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.32
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.11
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.05
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.17
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.58
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.10
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.56
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.32
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.62
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.49
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.99
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.53
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.10
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.90
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.65
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.84
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.38
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.15
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.98
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.53
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.17
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.09
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.32
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.56
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.70
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.27
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999945953
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.05
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999947954
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:39.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               7.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92274693.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56691
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.42
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.45
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.24
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.81
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.44
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.73
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.00
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.16
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.12
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.53
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.23
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.45
 p-value of test no 66                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.64
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.47
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908224
   j =  2                              :            45882
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908626
   j =  2                              :            45678
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 118                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.32
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.34
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.32
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.97
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.76
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.06
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.63
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.95
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.78
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.92
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.50
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.19
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.83
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.26
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.46
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.39
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.29
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.87
 p-value of test no 159                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.96
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.87
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.15
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.99
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.56
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.07
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.73
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.09
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.02
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.90
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.39
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.98
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.81
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.03
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.36
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.60
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.94
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.88
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.55
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.55
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.65
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 220                :    0.9951
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4647.62
 p-value of test no 222                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.40
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.95
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4342.41
 p-value of test no 228                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.06
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.88
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.27
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000006985
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.06
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999906419
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:16.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93290501.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56692
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9916
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.91
 p-value of test no 49                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.15
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.86
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.42
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.35
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.95
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.79
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.97
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.40
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.41
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.92
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.54
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46306
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870306
   j =  1                              :        399907390
   j =  2                              :            46302
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908170
   j =  2                              :            45906
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.99e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.15
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.95
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.90
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.47
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.68
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.78
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.76
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 126                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.86
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.07
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.66
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
 p-value of test no 142                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17685.72
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.21
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.71
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.93
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.94
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.49
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.81
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.36
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.01
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.77
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.67
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.31
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.51
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.40
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.33
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.99
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.35
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.01
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.93
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.91
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.85
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.97
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.42
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.22
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.72
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.33
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.53
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.89
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4725.87
 p-value of test no 173                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.05
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.31
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.96
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.75
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.18
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.57
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.82
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.37
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.70
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.73
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.80
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.35
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.20
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12195.70
 p-value of test no 229                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.71
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.11
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999965075
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.05
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000022600
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.021
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:11.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94306309.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56693
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9911
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.9901
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.91
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.38
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.08
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.53
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.75
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.81
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.67
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.86
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.45
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.13
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.19
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.03
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.02
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.22
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.20
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45339
 p-value of test no 70                 :    0.9942
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869339
   j =  1                              :        399909327
   j =  2                              :            45329
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908457
   j =  2                              :            45770
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 74                 :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  6.9e-3
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.85
 p-value of test no 119                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.02
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.61
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.33
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.38
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.44
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.25
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.16
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.49
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.75
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.40
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17202.65
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.68
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.28
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.37
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.92
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.14
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.88
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   54.22
 p-value of test no 153                :  6.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.44
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.32
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.55
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.96
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.93
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.85
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.09
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.43
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.81
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.94
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.32
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.35
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.68
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.26
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.79
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.11
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.42
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.53
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.29
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.21
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.68
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.15
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.13
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.17
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.44
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.42
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9731.91
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.050
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.89
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.95
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.84
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.76
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12187.43
 p-value of test no 229                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.13
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.23
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999884180
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.16
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000058375
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:47.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      6.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95354885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56694
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    5.34
 p-value of test no 44                 :  2.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.96
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.80
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.04
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.99
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.53
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.39
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.24
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.94
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.38
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.81
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.89
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.02
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.18
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907610
   j =  2                              :            46195
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45701
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908602
   j =  2                              :            45693
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.74
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.47
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.83
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.88
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.75
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.30
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.21
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.31
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.85
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17017.80
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.56
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.69
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.42
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.67
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.28
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.79
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.36
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.06
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.06
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.75
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.76
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.06
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.16
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.80
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.89
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.25
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.80
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.65
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.69
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4808.39
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.67
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.36
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.44
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.44
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.09
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.08
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.42
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.08
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.09
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 195                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.22
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.21
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.12
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.64
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.99
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4710.26
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.10
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.56
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.07
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12071.18
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.70
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000045886
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.81
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000032704
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:03.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  85  Fourier3, r = 27                0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96436229.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56695
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.11
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.32
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.51
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.96
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.05
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.38
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6868.20
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.01
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.63
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.53
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.75
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.42
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907927
   j =  2                              :            46035
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908332
   j =  2                              :            45831
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-6
 p-value of test no 109                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-5
 p-value of test no 113                :    0.9943
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.32
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.56
 p-value of test no 120                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.48
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.12
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.54
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.49
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.99
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.78
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.56
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.20
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17442.48
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.34
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.16
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.27
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.78
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.30
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.04
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.51
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.64
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.39
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.45
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.42
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.41
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.61
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.39
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.00
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.40
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.87
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.10
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.53
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.25
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.22
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.45
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.10
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.51
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.79
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.57
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.86
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.31
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.10
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.12
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.77
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.91
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.02
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.99
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.88
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.61
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.64
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.97
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.85
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.19
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999937211
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.82
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000091960
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:17.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97452037.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56696
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.92
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.23
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.97
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.91
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.62
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.94
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.39
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.46
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.61
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.81
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.83
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.59
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.52
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.28
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907781
   j =  2                              :            46099
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907992
   j =  2                              :            45998
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 79                 :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    4.65
 p-value of test no 81                 :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  1.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.70
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.78
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.32
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.20
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.37
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.05
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.22
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.94
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17718.27
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.38
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.77
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.96
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.05
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.28
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.33
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.21
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.03
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.42
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.38
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.35
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.85
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.76
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.40
 p-value of test no 159                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.81
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.22
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.50
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.11
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.45
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.82
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.18
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.94
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4827.42
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.28
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.23
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.89
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.86
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.20
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.86
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.45
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.67
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.37
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.10
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.26
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.46
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10343.24
 p-value of test no 211                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.13
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.60
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.07
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4359.33
 p-value of test no 227                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4388.43
 p-value of test no 228                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.19
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.35
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.45
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999971633
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.84
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000145459
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:19.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98467845.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56697
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.08
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.75
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.60
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.75
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.13
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.65
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.13
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.52
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.75
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7316.47
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.61
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.66
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.25
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.38
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908114
   j =  2                              :            45937
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908226
   j =  2                              :            45884
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.68
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.94
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.16
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.35
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.51
 p-value of test no 123                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.46
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.40
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.63
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.57
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.80
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.61
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.81
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.16
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.27
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.94
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.87
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.79
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.29
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.02
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.48
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.18
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.44
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.52
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.32
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.97
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.54
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.84
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.23
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.74
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.40
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.63
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.66
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.40
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.05
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.21
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.79
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.62
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.32
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.21
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.42
 p-value of test no 183                :  7.8e-3
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.37
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.66
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.20
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.27
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.35
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.06
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.06
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.48
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.29
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11532.04
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.80
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999872819
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.44
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999884246
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:18.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99450885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56698
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.89
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.24
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.84
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.51
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.17
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.69
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.84
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.03
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.57
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.96
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.35
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.08
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.51
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.39
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.22
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908243
   j =  2                              :            45877
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908300
   j =  2                              :            45850
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.47
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.04
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.95
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.17
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.09
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.96
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.89
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17585.69
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.89
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.17
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.03
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.48
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.31
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.07
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.94
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.14
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.88
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.73
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.23
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.60
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.04
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.93
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.36
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.77
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.25
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.93
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.72
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.41
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.24
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.41
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.06
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.67
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.31
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.66
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.79
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.12
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.69
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.96
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
 p-value of test no 185                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 187                :  4.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.21
 p-value of test no 188                :  6.7e-4    *****
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.00
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.43
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.74
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.23
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.67
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.94
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.12
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.02
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.89
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12119.01
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.29
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.31
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999878561
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.36
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999972209
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:52.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  83  LempelZiv, r = 15               6.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100499461.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56699
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 10                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    3.36
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.54
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.12
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.46
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.74
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.77
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.83
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.60
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.81
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.12
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.97
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.87
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.32
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.73
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908516
   j =  2                              :            45736
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908333
   j =  2                              :            45829
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.83
 p-value of test no 119                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.34
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.88
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.52
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.38
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.25
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.20
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.64
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.32
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.59
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.56
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.98
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.26
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.61
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.46
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.22
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.00
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.89
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.94
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.43
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.82
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.03
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.87
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.45
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.20
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.48
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.55
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.40
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.49
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.01
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.61
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.43
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.03
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.11
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.64
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.91
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.62
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.06
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.08
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.82
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.90
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.31
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.09
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.75
 p-value of test no 217                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.92
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.24
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.46
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.37
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.63
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.89
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.69
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000036259
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.53
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999970751
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -2.92e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:55.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101515269.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56700
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.75
 p-value of test no 41                 :  1.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.09
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.30
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.50
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.01
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.78
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.76
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.09
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.64
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.82
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.99
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.83
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.83
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.11
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908355
   j =  2                              :            45818
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908699
   j =  2                              :            45640
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.49
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.64
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.58
 p-value of test no 121                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.23
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.21
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.08
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.05
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.28
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.95
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.11
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17249.48
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.28
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.73
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.75
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.50
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.05
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.72
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.84
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.32
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.65
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.49
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.72
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.08
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.01
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.25
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.10
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.25
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.61
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.43
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.69
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  479.76
 p-value of test no 167                :  6.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.98
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.12
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.44
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.91
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.21
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.04
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.63
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.25
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.44
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.28
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.16
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.70
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.07
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.67
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.57
 p-value of test no 217                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.44
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.62
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.65
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.60
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.33
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.88
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.43
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000016660
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.35
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999958553
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:51.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 M (L=10000, r=0)    6.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82739225.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56701
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 6                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.96
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.39
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.15
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.60
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.78
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.96
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.78
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.64
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.84
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.83
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.45
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.51
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.15
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908405
   j =  2                              :            45784
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908034
   j =  2                              :            45980
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 115                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.29
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.74
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.48
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.05
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.95
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.08
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.31
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.90
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.64
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.78
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.96
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.91
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.80
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.80
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.74
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.74
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.90
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.45
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.58
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.45
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.97
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  598.44
 p-value of test no 163                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.73
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.87
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.86
 p-value of test no 166                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.78
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.82
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.57
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.94
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.49
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.38
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.97
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.61
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.59
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.69
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.69
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.26
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.00
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-3
 p-value of test no 208                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 209                :  2.6e-3
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 210                :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10391.58
 p-value of test no 211                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.66
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.29
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.79
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.73
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.62
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.17
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.70
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.66
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000117550
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.27
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999796379
 
 Normal statistic for number of bits   :   -1.61
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:25.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83230745.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56702
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.66
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.76
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.65
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.60
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.03
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.72
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.79
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6929.28
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.71
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.28
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.45
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.97
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908149
   j =  2                              :            45921
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908533
   j =  2                              :            45726
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.80
 p-value of test no 119                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.08
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.46
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.03
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.12
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.28
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.10
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.43
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.01
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.97
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.39
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.35
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.35
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.44
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.28
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.71
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.60
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.85
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.30
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.86
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.48
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.76
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.76
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.37
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.71
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.76
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.04
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.49
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.15
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.87
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.91
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.19
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.04
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.10
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.97
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.08
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.65
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.77
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.49
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.47
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.01
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.59
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.17
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.19
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.94
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.95
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.07
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.60
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000075454
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.22
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999959096
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:50.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84279312.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56703
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.73
 p-value of test no 23                 :  4.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.97
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.53
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.34
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.74
 p-value of test no 49                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   93.26
 p-value of test no 50                 :  7.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.07
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.77
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.99
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1307.65
 p-value of test no 56                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6976.77
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.18
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.31
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.68
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.83
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.37
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908421
   j =  2                              :            45785
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908351
   j =  2                              :            45817
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 91                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.50e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.32e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.45
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.39
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.78
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.11
 p-value of test no 122                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.87
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.69
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.96
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.11
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.36
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.96
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.54
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.32
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.01
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.37
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.10
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.98
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.23
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.79
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.75
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.92
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.39
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.55
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.71
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.13
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.25
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.04
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.86
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.22
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.34
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.90
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.49
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.74
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.14
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.08
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.65
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.38
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.53
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.67
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.96
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.54
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.70
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.53
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.73
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.62
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.53
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-3
 p-value of test no 205                :    0.9990
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.52
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.03
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.32
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.81
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.88
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.75
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.54
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.47
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.53
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.57
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999986033
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.92
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000045196
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.15
 p-value of test no 239                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:23.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          7.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85852176.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56704
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 5                  :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1517
 p-value of test no 12                 :  2.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334637
   j =  1                              :        599996967
   j =  2                              :             1515
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    5.01
 p-value of test no 26                 :  2.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    4.10
 p-value of test no 45                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.01
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.50
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.21
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.50
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.40
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.76
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.11
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.63
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.25
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.93
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7231.56
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.45
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.24
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.47
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.03
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46205
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870205
   j =  1                              :        399907596
   j =  2                              :            46193
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45578
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869578
   j =  1                              :        399908846
   j =  2                              :            45574
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
 p-value of test no 100                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.88
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.77
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.40
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.74
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.64
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.97
 p-value of test no 125                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.37
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.29
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.35
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.50
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.54
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.51
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.48
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.31
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.88
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.18
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.20
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.71
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.91
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.10
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.74
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.46
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.72
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.31
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.50
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.24
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.41
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.29
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.77
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.28
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.68
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.16
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.34
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.92
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.33
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.00
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.46
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.46
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.75
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.05
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.05
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.94
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.80
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.87
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.21
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.74
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.25
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12042.26
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.14
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.25
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999975926
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.08
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000120274
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:16.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            0.9992 
  12  CollisionOver, t = 21           2.5e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86933520.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56705
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    3.23
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.05
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.11
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.82
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.80
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.70
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.10
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.65
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.34
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.41
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.05
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.82
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.03
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908467
   j =  2                              :            45765
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46181
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870181
   j =  1                              :        399907646
   j =  2                              :            46165
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.09
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.81
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.03
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.63
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.16
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.96
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.60
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17400.02
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.13
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   52.30
 p-value of test no 148                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.12
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.70
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.03
 p-value of test no 151                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.87
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.10
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.32
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.05
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.17
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.41
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.25
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  424.83
 p-value of test no 163                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.60
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.87
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.25
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.05
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.90
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.89
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.33
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.56
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.19
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.73
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.13
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.29
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.26
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.53
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.64
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.81
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.16
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.41
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.29
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.41
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.64
 p-value of test no 226                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.74
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.37
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.57
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.41
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.47
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999974144
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.84
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000189085
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:40.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87851024.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56706
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5221
 p-value of test no 13                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 28                 :    0.9982
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 40                 :    0.9942
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.95
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.05
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.79
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.26
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.74
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.26
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.76
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1540.12
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.61
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.81
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.79
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.98
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.62
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45663
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908675
   j =  2                              :            45661
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908458
   j =  2                              :            45765
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-5
 p-value of test no 109                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.92
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.26
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.69
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.17
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.24
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.52
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.39
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.86
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.48
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.82
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.37
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.25
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.00
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.18
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.17
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.37
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.01
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.90
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.42
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.22
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.53
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.12
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.58
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.81
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.18
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   92.90
 p-value of test no 164                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.56
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.46
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.21
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.44
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.48
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.52
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.59
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.20
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.81
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.59
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.58
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.10
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 185                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.09
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.71
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.01
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.05
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.06
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.59
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.52
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.47
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.57
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.54
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.65
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.33
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999956498
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.66
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000002002
 
 Normal statistic for number of bits   :   0.016
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:45.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88899600.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56707
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 16                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 32                 :    0.9943
 
 Stat. AD after spacings (mNP2-S)      :    3.27
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.87
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.83
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.96
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.88
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.33
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.56
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.72
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.09
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.20
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.40
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.04
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.68
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.42
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.30
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.25
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.71
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.03
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908684
   j =  2                              :            45658
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907665
   j =  2                              :            46166
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.22
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.72
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.24
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.47
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.50
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.47
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.52
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.16
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17230.11
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.34
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.19
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.75
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.73
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.01
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.98
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.80
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.81
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.07
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.42
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.84
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.74
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.38
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.24
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.77
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.63
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.83
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.17
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.96
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.60
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.78
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.63
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.22
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.37
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.90
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.37
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.26
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.73
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.65
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-4
 p-value of test no 193                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.95
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.21
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.55
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.30
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.86
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.91
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.79
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.23
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.97
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.06
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12097.66
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.21
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.04
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999903947
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.60
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000187330
 
 Normal statistic for number of bits   :    1.48
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:29.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89915408.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56708
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.40
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.00
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.32
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.33
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.50
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.94
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.37
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.00
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.25
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.02
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.91
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908805
   j =  2                              :            45593
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908473
   j =  2                              :            45759
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
 p-value of test no 76                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 78                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 115                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.67
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.31
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.28
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.51
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.64
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.85
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.59
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.06
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.86
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.66
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.14
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.36
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.41
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.63
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.06
 p-value of test no 153                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.68
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.11
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.43
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.09
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.56
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.30
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.75
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.22
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.76
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.83
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.34
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.82
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.07
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.24
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.85
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.57
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.35
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.23
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.16
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.12
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.68
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.47
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    2.19
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.57
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.12
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.14
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.44
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.35
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.11
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.66
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.87
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.69
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.56
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.45
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.52
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000003094
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.41
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999980846
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.40
 p-value of test no 248                :    0.9919
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:15.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90898448.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56709
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 10                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7569
 p-value of test no 19                 :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.15
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.10
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.94
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.50
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.39
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.47
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6865.51
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.91
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.90
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.99
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.32
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.57
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908695
   j =  2                              :            45648
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45568
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869568
   j =  1                              :        399908870
   j =  2                              :            45556
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.11
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.46
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.60
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.31
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.34
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.71
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.21
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.17
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.38
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.40
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.99
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.17
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.56
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.04
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.75
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.52
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.55
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.41
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.26
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.17
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.72
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.42
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.08
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.91
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.16
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.21
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.86
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.46
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.21
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.71
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.42
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.96
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.23
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.18
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.19
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.75
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.09
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.42
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.08
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.04
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.74
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.41
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
 p-value of test no 209                :    0.9985
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9641.81
 p-value of test no 211                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.52
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.01
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.46
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.56
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.38
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.00
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.19
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.66
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000083299
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.47
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000038455
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:35.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91881488.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56710
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    4.45
 p-value of test no 33                 :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.08
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.48
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.55
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.51
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.27
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.62
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.81
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.05
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.36
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6931.01
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.40
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.74
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.69
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.32
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5284.52
 p-value of test no 68                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907784
   j =  2                              :            46096
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908558
   j =  2                              :            45718
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.65
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.96
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.95
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.43
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.59
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.10
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.98
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.26
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.54
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.70
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.67
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.92
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.63
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.96
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.84
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.27
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    6.33
 p-value of test no 153                : 1 -  5.8e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.26
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.31
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.23
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.96
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.66
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.63
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.21
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.75
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.27
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.30
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.91
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.11
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.03
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.38
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.59
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.55
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.56
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.18
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.23
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.18
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 185                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.03
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.72
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.92
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.51
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.52
 p-value of test no 218                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.34
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.66
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.82
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.38
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.80
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.87
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000068638
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.53
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000050185
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:11.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)     1 -  5.8e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92864528.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56711
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5288
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.34
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.59
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.08
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.36
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.73
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.02
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.60
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.67
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.16
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.21
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.58
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.47
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.77
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.77
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908412
   j =  2                              :            45788
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907957
   j =  2                              :            46017
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 104                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-3
 p-value of test no 107                :    0.9990
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.31
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.42
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.21
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.67
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.53
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.68
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.76
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.40
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.70
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.38
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.86
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.25
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.48
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.58
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.58
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.26
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.21
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.51
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.16
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.52
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.83
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.98
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.84
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.76
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.07
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.14
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.18
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.91
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.96
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.62
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.80
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.83
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.12
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.69
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.95
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.15
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.52
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.65
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.46
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.22
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 191                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.16
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.48
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.61
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.16
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10282.62
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.60
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.07
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.10
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.44
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.11
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.48
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.31
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.35
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000137755
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.59
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999920372
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:09.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93716484.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56712
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.92
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.01
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.21
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.84
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.52
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.78
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.00
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.29
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.68
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.57
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.69
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.82
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.39
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46279
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870279
   j =  1                              :        399907447
   j =  2                              :            46269
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908301
   j =  2                              :            45842
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-3
 p-value of test no 90                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 92                 :  3.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 103                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 105                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.78
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.29
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.75
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.07
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.76
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.86
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.29
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.74
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.28
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.02
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.78
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.85
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.61
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.12
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.99
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.25
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.09
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.95
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.74
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.29
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.48
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.21
 p-value of test no 158                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.09
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.22
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.39
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.44
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.05
 p-value of test no 163                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.76
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.28
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.54
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.18
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.14
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.27
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.08
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.47
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.91
 p-value of test no 172                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.23
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.34
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.20
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.58
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.16
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.52
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.82
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.73
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.04
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.01
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.24
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.13
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.47
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.25
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.63
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000034543
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.73
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999978536
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:33.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94765060.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56713
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 4                  :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    4.27
 p-value of test no 24                 :  6.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     837
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.81
 p-value of test no 35                 :  3.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.72
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.72
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.03
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.98
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.62
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.77
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.55
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.61
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.98
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.14
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.63
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.46
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.58
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.88
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.45
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46164
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907678
   j =  2                              :            46152
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 86                 :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    5.10
 p-value of test no 88                 :  2.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9953
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 106                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-5
 p-value of test no 109                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.54
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.60
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.64
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.36
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.90
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.88
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.49
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.49
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.57
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-4
 p-value of test no 139                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.73
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17642.23
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.45
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.27
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.85
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.43
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.66
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.91
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.84
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.20
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.54
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.93
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.83
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.43
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.36
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.15
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.93
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.72
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.91
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.55
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.05
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.24
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.94
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.61
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.96
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.01
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.07
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.55
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.80
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.88
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.85
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.46
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.59
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.29
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.87
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.81
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.05
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.56
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.40
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.15
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.26
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.06
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999867344
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000037423
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:40.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95715332.
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                  Starting BigCrush
                  Version: TestU01 1.2.3
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                     Run no 56714
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.03
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.65
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.88
 p-value of test no 49                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.66
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.11
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.33
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6854.15
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.76
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.51
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.10
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.91
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5220.54
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908403
   j =  2                              :            45794
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46326
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870326
   j =  1                              :        399907352
   j =  2                              :            46318
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.26
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.09
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.41
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.02
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.58
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.19
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.47
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.08
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.45
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.75
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.75
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.63
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.51
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.87
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.93
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.70
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.07
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.95
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.62
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.92
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.45
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.03
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.00
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.72
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.84
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.38
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.97
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.47
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.64
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.08
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.26
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.32
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.53
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.99
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.01
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.55
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.66
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.75
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.21
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.73
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.67
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.87
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.99
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.93
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.76
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.73
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.28
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.13
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.59
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.36
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999929681
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.31
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999910466
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-3
 p-value of test no 236                :    0.9981
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.22
 p-value of test no 244                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96763908.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56715
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 10                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.45
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.81
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.00
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.06
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.05
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.80
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.99
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7154.52
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.55
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 63                 :    0.9917
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   36.89
 p-value of test no 65                 :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.87
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.94
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908174
   j =  2                              :            45907
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45377
 p-value of test no 71                 :    0.9905
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869377
   j =  1                              :        399909249
   j =  2                              :            45371
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.80
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.75
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.75
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.58
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 131                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.65
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.87
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.47
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17566.92
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.64
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.10
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.95
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.60
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.27
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.82
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.60
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.20
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.66
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.14
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.27
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.04
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.35
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.76
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.20
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.67
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.92
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.79
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.91
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.61
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.91
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.47
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.53
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.35
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.01
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.02
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.96
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.23
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.63
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.14
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.05
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.73
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.55
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5148.62
 p-value of test no 226                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.57
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.97
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.63
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.16
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.04
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000002212
 
 Normal statistic for number of bits   :   0.017
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.32
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999821486
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:19.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97746948.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56716
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    3.52
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.29
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.78
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.37
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.51
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.82
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.89
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.90
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.54
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.95
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.36
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.42
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.62
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4838.14
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908673
   j =  2                              :            45659
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46274
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870274
   j =  1                              :        399907453
   j =  2                              :            46272
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.44
 p-value of test no 119                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.70
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.80
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.49
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.64
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.04
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.89
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.90
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.90
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.83
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.88
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.54
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.69
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.11
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.59
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.07
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.46
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.60
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.13
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.65
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.49
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.81
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.73
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.84
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.32
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.72
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.63
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.82
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.72
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.07
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.58
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.78
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.42
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.44
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.94
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.06
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.34
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.33
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.60
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.87
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.57
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.42
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.36
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 218                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 219                :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 221                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4634.35
 p-value of test no 222                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.59
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.65
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.58
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.82
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.88
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.17
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999883403
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999886064
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-3
 p-value of test no 246                :    0.9987
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.63
 p-value of test no 248                :    0.9958
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:08.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98697220.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56717
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    3.03
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.05
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.22
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.80
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.45
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.99
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.85
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.71
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1577.98
 p-value of test no 56                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.43
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.42
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.39
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.15
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.51
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907750
   j =  2                              :            46116
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908459
   j =  2                              :            45766
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-4
 p-value of test no 112                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.52
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.23
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.48
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.53
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.00
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.10
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.27
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.63
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 139                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.18
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17445.37
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.66
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.69
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.37
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.43
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.41
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.17
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.68
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.81
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.52
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.91
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.54
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.59
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.01
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.06
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.99
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.38
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.55
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.95
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.31
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.22
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.77
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.23
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.96
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.70
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.77
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.78
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.84
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.65
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.02
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.15
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.86
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.85
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 202                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.99
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.82
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.03
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.75
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.34
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.37
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.90
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.12
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.35
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.58
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.21
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000085891
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.57
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000119869
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:56.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99713028.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56718
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.68
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    3.55
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.04
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.58
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.67
 p-value of test no 49                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.05
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.07
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.47
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.39
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.02
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.89
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.27
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
 p-value of test no 62                 :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.62
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.34
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4928.27
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45608
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869608
   j =  1                              :        399908789
   j =  2                              :            45598
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908044
   j =  2                              :            45972
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.06
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.59
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.05
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.15
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.01
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.47
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.42
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.94
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.73
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17322.80
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.05
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.08
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.51
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.05
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.14
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.25
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.27
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.15
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.87
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.19
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.75
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.42
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.81
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.46
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.91
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.37
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.30
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.18
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.51
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.68
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.77
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.98
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.16
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.89
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.13
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5280.99
 p-value of test no 173                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.20
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.47
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.41
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.73
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.46
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.42
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.81
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 210                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.58
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.41
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.32
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.32
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.62
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.99
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.97
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.05
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.26
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000000262
 
 Normal statistic for number of bits   : 2.07e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.57
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000039877
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:28.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100696081.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56719
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1477
 p-value of test no 12                 :  1.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334597
   j =  1                              :        599997046
   j =  2                              :             1477
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7135
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.52
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     834
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   25.03
 p-value of test no 46                 :  7.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.17
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.81
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.06
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.41
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.86
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.75
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.16
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.48
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.64
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.93
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.56
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.40
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4791.20
 p-value of test no 68                 :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908193
   j =  2                              :            45902
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908339
   j =  2                              :            45820
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.44
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.07
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.08
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.04
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.26
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.35
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.96
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.26
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.59
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.18
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.00
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.26
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.93
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.31
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.87
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.14
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.70
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.67
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.97
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.02
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.34
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.06
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.63
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.86
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.86
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.64
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.40
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.83
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.45
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.64
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.09
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.20
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.01
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.04
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.23
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.91
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.81
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 185                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.87
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.11
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.83
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.88
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.53
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.29
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.62
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.25
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.06
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.44
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.82
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.06
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000123001
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.58
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999918101
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.077
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:15.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                7.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101875729.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56720
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4492
 p-value of test no 14                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 21                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.46
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.32
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.57
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.68
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.37
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.08
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.08
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.47
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.87
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.58
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.00
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.62
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.34
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.98
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46281
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870281
   j =  1                              :        399907444
   j =  2                              :            46269
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908028
   j =  2                              :            45977
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 97                 :  7.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 98                 :    0.9934
 
 Anderson-Darling statistic = A2       :    4.56
 p-value of test no 99                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.81
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.21
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.74
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.54
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.58
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.34
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.11
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.40
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.38
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.30
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.85
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.08
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.53
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.42
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.59
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.34
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.22
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.88
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.00
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.16
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.65
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.29
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.71
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.21
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.33
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  470.29
 p-value of test no 166                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.71
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5269.27
 p-value of test no 168                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.51
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.67
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.51
 p-value of test no 171                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.51
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.31
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.24
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  145.52
 p-value of test no 175                :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.47
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.63
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 186                :    0.9933
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.69
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.87
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.62
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.31
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.79
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.97
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.90
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.33
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.01
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.63
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.33
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.91
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.05
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000018661
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.56
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000059239
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:57.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82771994.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56721
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 5                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    3.66
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.47
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.88
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.05
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.95
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.02
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.82
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.74
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.52
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.01
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.33
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.56
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.83
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.03
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.31
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.50
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908271
   j =  2                              :            45863
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908356
   j =  2                              :            45819
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.09
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.03
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.29
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.85
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.55
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.76
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.02
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.73
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.01
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.53
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.47
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.23
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.91
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.12
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.87
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.83
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.30
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.86
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.57
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.27
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.43
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.51
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.52
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.47
 p-value of test no 162                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.21
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.56
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.38
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.97
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.11
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.42
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.27
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.12
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.77
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.17
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.79
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.56
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.34
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.83
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.93
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.23
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.41
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.54
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.89
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.75
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.73
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.63
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.62
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.90
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.71
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000113575
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.72
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999871439
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:24.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83361818.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56722
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.42
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.49
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.13
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.48
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.93
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.43
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.74
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.12
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.83
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6879.63
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.00
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.04
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.17
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.47
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5175.66
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46310
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870310
   j =  1                              :        399907384
   j =  2                              :            46302
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908131
   j =  2                              :            45930
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
 p-value of test no 103                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.63
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.13
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.98
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.48
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.74
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.16
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.86
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.60
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17357.00
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   74.34
 p-value of test no 146                :  1.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.58
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.67
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.09
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.17
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.77
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.40
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.73
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.53
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.78
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.26
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.17
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.96
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.28
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.39
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.84
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.21
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.87
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.12
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.21
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.90
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.69
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.64
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.84
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.12
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.83
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.20
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.14
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.70
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.58
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.27
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.12
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.78
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10305.03
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.45
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.41
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.67
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.14
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.12
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.52
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.11
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000087778
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.09
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000077563
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    2.01
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:40.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       1.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84115482.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56723
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.68
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.98
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.51
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.19
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.46
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.99
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.31
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.53
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.93
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.11
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.38
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.38
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.61
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.92
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.13
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.67
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.21
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908261
   j =  2                              :            45862
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907985
   j =  2                              :            45997
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.16
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.32
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.12
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.95
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.68
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 132                :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.85
 p-value of test no 133                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.77
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.44
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.08
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.03
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.21
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.33
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.13
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.40
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.58
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.39
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.99
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.00
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.00
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.74
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.74
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.64
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.37
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.04
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.52
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.23
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.84
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.69
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.32
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.11
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4822.68
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.57
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.66
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.02
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.33
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.69
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.54
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.56
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.44
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.71
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.95
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.48
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.25
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.06
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.37
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.93
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.13
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.14
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.29
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.34
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.41
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000039838
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.19
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000023869
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.024
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:01.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85032986.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56724
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.34
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.17
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.83
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.40
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.58
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.84
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.70
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.40
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.17
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.35
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.41
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.86
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.93
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.67
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46317
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870317
   j =  1                              :        399907369
   j =  2                              :            46311
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908199
   j =  2                              :            45890
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 91                 :    0.9915
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.53
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.05
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.79
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.24
 p-value of test no 122                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.16
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.64
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.55
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.16
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.17
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.39
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  173.68
 p-value of test no 141                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.92
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.32
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   69.77
 p-value of test no 147                :  4.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.75
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.63
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.27
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.86
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.12
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.18
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.27
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.32
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.22
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.62
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.13
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.60
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.98
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.25
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.15
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.16
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.72
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.36
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.46
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.63
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.34
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.55
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.16
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.33
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.49
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.49
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.71
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.05
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.42
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.68
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.90
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.67
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.30
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.93
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.95
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.73
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.71
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.55
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.97
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000081166
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.14
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999995276
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.015
 p-value of test no 238                :    0.51
 
 Sample variance                       :    2.21
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:25.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       4.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85983258.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56725
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.37
 p-value of test no 28                 :  5.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.38
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.76
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.27
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.04
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.30
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.14
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.99
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.73
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.48
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.49
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.63
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.36
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.09
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.62
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.16
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907826
   j =  2                              :            46084
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907941
   j =  2                              :            46025
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.05
 p-value of test no 117                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.46
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.94
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.25
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.26
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.17
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.69
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 134                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.31
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.64
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17804.85
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.88
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.66
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.04
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.55
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.23
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.62
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.22
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.58
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.72
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.80
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.62
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.03
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.89
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.17
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.97
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.79
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.73
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.78
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.10
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.34
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.57
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.03
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.48
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.40
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.82
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.62
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.10
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.54
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.48
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.65
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.14
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.14
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.68
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.01
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.48
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.67
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.10
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.37
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.95
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000101044
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.10
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000069526
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:53.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87031834.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56726
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 9                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5555
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 15                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    3.47
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.83
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.41
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.26
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.37
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.28
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.63
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.18
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.71
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.04
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.02
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.76
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.26
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.74
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907798
   j =  2                              :            46098
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 72                 :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.02
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.14
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.67
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.96
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.99
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.64
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.40
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.25
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.39
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17212.25
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.29
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.81
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.67
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.69
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.40
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.85
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.22
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.21
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.14
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.21
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.66
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.13
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.34
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.63
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.04
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.98
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.53
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.59
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.55
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.29
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.10
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.26
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.20
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.78
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.21
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.83
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.32
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.38
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.49
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.09
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.86
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.10
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.49
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.89
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10272.09
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.74
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.70
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.56
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.07
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.59
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.26
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.70
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.65
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999945764
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.46
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000058159
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.20
 p-value of test no 254                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:58.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88637466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56727
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    3.39
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.57
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.14
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.39
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.68
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.02
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.91
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.53
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.55
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.37
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.26
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.30
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.76
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.29
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.92
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908008
   j =  2                              :            45993
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908582
   j =  2                              :            45706
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.10
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.00
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.41
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.05
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.79
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.03
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.56
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  175.11
 p-value of test no 141                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17575.11
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.60
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.45
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.13
 p-value of test no 148                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.67
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.88
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.76
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.89
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.92
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.03
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.62
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.55
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.79
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.44
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.23
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.50
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.01
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.38
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.35
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.04
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.85
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.60
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.45
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.21
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.69
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.29
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.83
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.74
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.06
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.72
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.92
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 200                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.46
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.08
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.86
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.77
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.55
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.82
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.75
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.46
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.08
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.84
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.14
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000040594
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.87
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999965909
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.99
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:39.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89653274.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56728
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 6                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7114
 p-value of test no 18                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7612
 p-value of test no 21                 :  3.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.13
 p-value of test no 36                 :    0.9996    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.46
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.76
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.61
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.09
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.47
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.71
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.00
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.70
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.19
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.02
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.33
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.70
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.20
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.76
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908274
   j =  2                              :            45851
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908496
   j =  2                              :            45746
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.91
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.79
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.96
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.39
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.91
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.05
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.18
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.74
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17304.91
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.57
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.96
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.45
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.53
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.18
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.78
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.48
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.58
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.38
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.16
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.65
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.95
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.16
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.99
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.42
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.59
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.23
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.37
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.71
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.15
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.29
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.18
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.59
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.02
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.37
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.31
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.60
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.35
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.06
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.80
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.52
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.42
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.34
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.81
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.60
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.65
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.68
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.90
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.20
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.25
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.02
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999879740
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.92
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000064096
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:28.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        3.3e-4
  24  ClosePairs mNP1, t = 9          0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90636314.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56729
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 7                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 39                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.74
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.73
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.18
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.57
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.40
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.42
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.00
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.87
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.47
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.44
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.06
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.78
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908252
   j =  2                              :            45868
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46290
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870290
   j =  1                              :        399907422
   j =  2                              :            46286
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.31
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.10
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.29
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.73
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.41
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.91
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.84
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.04
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  170.09
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17744.31
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.20
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.72
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.62
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.01
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.34
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.46
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.35
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.84
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.82
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.40
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.73
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.61
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.45
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.48
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.71
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.54
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.50
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.80
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.12
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.73
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.96
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.92
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.83
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.13
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.52
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.01
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.53
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.87
 p-value of test no 178                :  1.4e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.91
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.90
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.05
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9701.42
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.67
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.75
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.49
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.83
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.31
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.92
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.80
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000089692
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.91
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999974519
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 235                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 236                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 237                :  4.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.98
 p-value of test no 238                :  1.4e-3
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:33.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91717658.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56730
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.79
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.46
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.67
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.79
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.18
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.64
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.91
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.92
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.78
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.62
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.09
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.02
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.82
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.42
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5160.52
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908152
   j =  2                              :            45918
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908033
   j =  2                              :            45979
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.84
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.75
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.93
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.10
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.86
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.31
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.37
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.61
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17088.04
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.39
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.14
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.17
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.97
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.16
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.92
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.75
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.88
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.11
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.83
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.57
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.29
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.24
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.04
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.47
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.11
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.52
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.91
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.38
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.23
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.07
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.08
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.84
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.15
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.37
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.33
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.31
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.36
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.96
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.44
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.46
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9754.80
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.85
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.34
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.21
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.34
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.33
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.02
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.66
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000088438
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.98
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000115504
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:23.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92733466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56731
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 9                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.92
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    4.90
 p-value of test no 24                 :  3.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 29                 :    0.9974
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.97
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.30
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.25
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.67
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.28
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.28
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.01
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.50
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.18
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.98
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.93
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 58                 :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 60                 :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   57.13
 p-value of test no 61                 :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.96
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.41
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.16
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.55
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908376
   j =  2                              :            45806
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908103
   j =  2                              :            45947
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.84
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.57
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.28
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.22
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.23
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.82
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.97
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.069
 p-value of test no 135                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.20
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17550.67
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.21
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.96
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.94
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.09
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.78
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.03
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.46
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.40
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.67
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.74
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.29
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.48
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.32
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.63
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.87
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.96
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.02
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.58
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.15
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.51
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.60
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.45
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.41
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.96
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.86
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.24
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.45
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.69
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.04
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.26
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.51
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.39
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.94
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.59
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.98
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.46
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.73
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.08
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.82
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.33
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000029998
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.85
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999891401
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:38.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93618202.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56732
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    3.15
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    4.83
 p-value of test no 27                 :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.34
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.39
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.74
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.57
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.23
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.23
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.60
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.14
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.53
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.44
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.78
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.48
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.70
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908221
   j =  2                              :            45882
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908345
   j =  2                              :            45823
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 93                 :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-4
 p-value of test no 94                 :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    5.38
 p-value of test no 95                 :  2.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9998    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.72
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.02
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.67
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.48
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.55
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.27
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.67
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.58
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.73
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 142                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 144                :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16992.93
 p-value of test no 145                :    0.9908
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.95
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.25
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.79
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.21
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.95
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.18
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.50
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.91
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.90
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.61
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.53
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.58
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.78
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.90
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.33
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.83
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.11
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.82
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.06
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.20
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.00
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.28
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.67
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.98
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.71
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.52
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.73
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.70
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.02
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.01
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.60
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.03
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.42
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.14
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.22
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.08
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.43
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.01
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.30
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.70
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.02
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000023644
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.07
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000068410
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.56e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:55.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  0.9998 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94666778.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56733
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.93
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.85
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.50
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.38
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.05
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.44
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.73
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.00
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.27
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.59
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.06
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.47
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.72
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908482
   j =  2                              :            45756
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46302
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870302
   j =  1                              :        399907400
   j =  2                              :            46294
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.29
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.18
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.99
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.56
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.20
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.02
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.28
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.61
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.83
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.89
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.31
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.49
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.48
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.87
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.67
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.71
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.36
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.64
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.47
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.52
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.55
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.65
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.22
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.09
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.48
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.39
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.02
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.40
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.95
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.32
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.09
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.34
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.53
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.06
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.94
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.88
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.07
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.13
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.49
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.00
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.07
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.64
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.92
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.41
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.55
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5128.69
 p-value of test no 222                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5132.83
 p-value of test no 226                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.10
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.17
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.73
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.81
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.37
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999954653
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.97
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000024709
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:45.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95617050.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56734
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.40
 p-value of test no 46                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.61
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.88
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.24
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.04
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.60
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.88
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.87
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6891.67
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.01
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.58
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.20
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.33
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45347
 p-value of test no 70                 :    0.9936
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869347
   j =  1                              :        399909306
   j =  2                              :            45347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907801
   j =  2                              :            46098
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 81                 :  8.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  6.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 103                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.30
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.78
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.63
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.67
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.69
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.31
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.15
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.81
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.60
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.55
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17533.27
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.96
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.02
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.13
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.55
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.37
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.03
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.21
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.34
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.87
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.23
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.63
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.39
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.80
 p-value of test no 162                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.19
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.01
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.83
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.19
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.95
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.07
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.56
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.09
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.00
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.77
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.67
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.69
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.38
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.95
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.39
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.94
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 204                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.66
 p-value of test no 207                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.72
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.14
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5099.20
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.11
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.19
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.28
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.95
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.55
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.35
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999948092
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.29
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999999632
 
 Normal statistic for number of bits   : -2.91e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:31.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96632834.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56735
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 7                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5225
 p-value of test no 13                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9953
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.18
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.23
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.55
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.35
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.06
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.85
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.22
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.89
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.96
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.80
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.98
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.48
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.05
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.92
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.76
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4892.04
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908367
   j =  2                              :            45812
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908478
   j =  2                              :            45749
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 5.67e-4
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.94
 p-value of test no 119                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.94
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.06
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.13
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.11
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.81
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9967
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.29
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.50
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.32
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.17
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.78
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.59
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.33
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.60
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.12
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.63
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.89
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.34
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.65
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.69
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.98
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.10
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.40
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.04
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.22
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.61
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.08
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.64
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.36
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.49
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.54
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.96
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.83
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.23
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.06
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.90
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.71
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.03
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.91
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.28
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.36
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.06
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.65
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.85
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.18
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.46
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.77
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.60
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000051562
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.72
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999879191
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    2.00
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:57.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97878018.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56736
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.65
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.46
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.78
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.86
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.96
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1333.08
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.14
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.85
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.28
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.67
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.36
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.60
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907980
   j =  2                              :            46007
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907809
   j =  2                              :            46082
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.08
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.66
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.96
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.17
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.86
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.74
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17552.68
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.71
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.19
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.78
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.25
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.31
 p-value of test no 150                :    0.9909
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.03
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.38
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.18
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.89
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.31
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.83
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.74
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.95
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.04
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.94
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.21
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.53
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.01
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.21
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.61
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.36
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.52
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.28
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.39
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.19
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.10
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.22
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.86
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.46
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.94
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.21
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.90
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 219                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5101.22
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.70
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.83
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.18
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.75
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11542.82
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.64
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999827495
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.24
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000039010
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 241                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    4.42
 p-value of test no 242                :  5.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.54
 p-value of test no 243                :  5.6e-3
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.055
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98729986.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56737
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 9                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.09
 p-value of test no 29                 :  8.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    3.22
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.26
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.88
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.86
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.77
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.28
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.80
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.97
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7175.42
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.46
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.67
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.85
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.47
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.28
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907819
   j =  2                              :            46089
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907669
   j =  2                              :            46152
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.51
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.31
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.55
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.72
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.57
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.51
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.62
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.53
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.27
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.58
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.75
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.52
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.71
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.82
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.00
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.75
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.86
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.00
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.25
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.88
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.89
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.69
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.82
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.67
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.76
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.41
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.67
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.86
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.82
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.13
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.39
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.80
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.72
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.23
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.86
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.60
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.78
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.28
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.94
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.68
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.78
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 216                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.63
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.26
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.05
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.93
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.73
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.93
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.15
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999810710
 
 Normal statistic for number of bits   :   -1.50
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.01
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000036583
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:54.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99745794.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56738
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.14
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.11
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.02
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.63
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.72
 p-value of test no 53                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.54
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.90
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.89
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.32
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.02
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.53
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.10
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.45
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908023
   j =  2                              :            45987
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908096
   j =  2                              :            45943
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 104                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.40
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.42
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.92
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.44
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.82
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.55
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.32
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.11
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17443.41
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.53
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.49
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.63
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.29
 p-value of test no 151                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.58
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.68
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.22
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.49
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.96
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.02
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.54
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.39
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.71
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.24
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.41
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.11
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.99
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.11
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.83
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4739.31
 p-value of test no 168                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.93
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.97
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.75
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.98
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.69
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.38
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.41
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 181                :  3.7e-4    *****
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 182                :  9.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.85
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.03
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.34
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.17
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.95
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.69
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.31
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4675.97
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.48
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.66
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.18
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.00
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.29
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999992042
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.40
 p-value of test no 233                :  9.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000077236
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:26.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100728834.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56739
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 9                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 33                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.98
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.07
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.14
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.49
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.52
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.34
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.75
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.88
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1553.16
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.59
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.09
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.66
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.84
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.99
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.11
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908088
   j =  2                              :            45953
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907935
   j =  2                              :            46025
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 83                 :  9.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    6.65
 p-value of test no 85                 :  5.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.71
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.55
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.77
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.81
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.60
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.26
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.96
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.31
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.65
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.60
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.23
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.45
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.66
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.45
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.28
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.06
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.09
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.47
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.59
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.11
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.09
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.77
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.68
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.88
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.63
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.29
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.78
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.73
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.30
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.60
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.52
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.54
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.02
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.74
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.58
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.50
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.63
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.59
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.81
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.60
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.88
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.98
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.28
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.99
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.91
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.11
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.73
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000077422
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.52
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000155725
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:35.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft AD, t = 16               5.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101744642.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56740
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4503
 p-value of test no 16                 :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.40
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.64
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.51
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.66
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.60
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.45
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.43
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.35
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.03
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.19
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.79
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.14
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.10
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.24
 p-value of test no 67                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4876.70
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908586
   j =  2                              :            45701
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908365
   j =  2                              :            45810
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 87                 :  5.2e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.30
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.70
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.80
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.81
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.85
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.12
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.62
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 126                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.46
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.08
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.41
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.57
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.28
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.84
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.24
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.79
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.12
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.29
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.75
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.36
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.32
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.21
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.16
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.41
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.49
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.85
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.41
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.83
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.92
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.48
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.40
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.78
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.98
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.20
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.37
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.02
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.57
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.70
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.86
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.73
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.37
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.05
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.35
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.08
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.21
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.25
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.90
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.05
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3900.79
 p-value of test no 228                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.12
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.42
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.20
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000102529
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.10
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000052534
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:59.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  43  Permutation, t = 10             0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82804763.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56741
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997239
   j =  2                              :             1379
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    6.14
 p-value of test no 26                 :  8.5e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.04
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    4.36
 p-value of test no 36                 :  5.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     345
 p-value of test no 37                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.35
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.33
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.07
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.86
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.51
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.92
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.69
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.84
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.99
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.13
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908047
   j =  2                              :            45975
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908417
   j =  2                              :            45781
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 94                 :    0.9947
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9951
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-6
 p-value of test no 109                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.29
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.94
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.36
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.25
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.27
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.36
 p-value of test no 125                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.99
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.92
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.30
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.64
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 143                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 144                :  5.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17942.71
 p-value of test no 145                :  3.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.85
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.17
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.97
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.47
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.18
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.00
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.58
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.00
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.45
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.76
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.91
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.63
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.12
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.49
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.22
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.32
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.06
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.75
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.06
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.01
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.88
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.54
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.35
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.55
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.42
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.95
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.20
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.47
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.09
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.29
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.22
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.73
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.86
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.13
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.18
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3973.93
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.33
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.14
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.36
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000099085
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.20
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000043291
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:27.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          8.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83755035.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56742
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1486
 p-value of test no 11                 :  6.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334606
   j =  1                              :        599997028
   j =  2                              :             1486
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.63
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.50
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.67
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.60
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.61
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.36
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.10
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.35
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.82
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.64
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.97
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.35
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.69
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45575
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869575
   j =  1                              :        399908852
   j =  2                              :            45571
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908405
   j =  2                              :            45793
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.36
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.64
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.47
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.17
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.49
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.22
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.50
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.063
 p-value of test no 134                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.11
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.09
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.86
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.93
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.00
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.68
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.38
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.17
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.70
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.58
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.43
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.08
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.04
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.57
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.04
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.71
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.78
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.94
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.38
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.52
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.06
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.50
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.52
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.39
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.80
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.80
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.39
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.52
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.79
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.71
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.66
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.47
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 188                :    0.05
 
 Sample variance                       :    2.03
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.70
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.40
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.83
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.33
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.93
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.97
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.09
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.21
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.97
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.81
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12140.57
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.46
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000028615
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.98
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000217453
 
 Normal statistic for number of bits   :    1.72
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:29.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           6.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84607003.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56743
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.02
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.79
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.91
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.51
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.16
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.56
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.72
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.40
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.66
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6794.87
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.68
 p-value of test no 58                 :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.69
 p-value of test no 61                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.66
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.54
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.49
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.31
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907790
   j =  2                              :            46102
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.38
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.28
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.41
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.28
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.25
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.70
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.15
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17443.37
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.90
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.52
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.25
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.75
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.63
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.89
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.75
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.16
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.64
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.90
 p-value of test no 159                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.00
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.21
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.90
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.28
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.23
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.57
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.24
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.15
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.43
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.46
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.14
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.35
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.97
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.60
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.50
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.49
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.75
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.66
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.07
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.59
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.42
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4723.18
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4348.84
 p-value of test no 227                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.78
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.42
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12096.49
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.28
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999988844
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.41
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999946487
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:46.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85557250.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56744
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.52
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.59
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.05
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.13
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.32
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.53
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.03
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.22
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.00
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.78
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.54
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.29
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.24
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908852
   j =  2                              :            45568
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.91
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.86
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.55
 p-value of test no 122                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.70
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.41
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.08
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.13
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.36
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.14
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.81
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   56.18
 p-value of test no 148                :  3.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.11
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.47
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.37
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.92
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.99
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.23
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.46
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.19
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.88
 p-value of test no 157                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.86
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.48
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.95
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.97
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.53
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.24
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.28
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.86
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.04
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.70
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.82
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.24
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.98
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.97
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.39
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.92
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.97
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.94
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 181                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.25
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.47
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.18
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.85
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.32
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.93
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.54
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.17
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.99
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.58
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.46
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000046669
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.08
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999951662
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.066
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       3.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86573058.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56745
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    3.44
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.94
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.55
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.93
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.37
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.91
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.27
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.43
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.58
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7111.90
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.95
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.79
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.18
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.35
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.83
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908425
   j =  2                              :            45783
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908536
   j =  2                              :            45729
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.00
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.00
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.33
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.80
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 127                :    0.9929
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.61
 p-value of test no 129                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.64
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.66
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.28
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.96
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.27
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.68
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.14
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.86
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.15
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.72
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.86
 p-value of test no 154                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.66
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.65
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.17
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.48
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.84
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.44
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.61
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.04
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.74
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.22
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.71
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.75
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.22
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.22
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.18
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.34
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.22
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.84
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.04
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.14
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.64
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.58
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.84
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.33
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.46
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.22
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10218.48
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.31
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.47
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.07
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.54
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.01
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.55
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.27
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.34
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999920288
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.04
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000120919
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:41.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87457805.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56746
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 22                 :    0.9977
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.66
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.07
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.42
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.84
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.41
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.24
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.06
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.47
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.22
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.74
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.26
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.13
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.97
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.60
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.42
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908192
   j =  2                              :            45901
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46530
 p-value of test no 71                 :  1.2e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870530
   j =  1                              :        399906940
   j =  2                              :            46530
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.66
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.75
 p-value of test no 120                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.55
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.35
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.06
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.42
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.24
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.30
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.14
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.34
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.52
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.13
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.65
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.15
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.68
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.91
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.93
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.85
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.56
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.48
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.65
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.47
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.28
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.59
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.94
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.14
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.03
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5275.23
 p-value of test no 168                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.17
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.00
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.64
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.84
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.46
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.53
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.85
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.33
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 186                :    0.9958
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.56
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.36
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.64
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.73
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.40
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.20
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.66
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.62
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12096.62
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.70
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.42
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999873809
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.28
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999982979
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.067
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:44.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88342541.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56747
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.23
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.97
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.22
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.29
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.77
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.01
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.59
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.36
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.79
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.69
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.43
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.90
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.62
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.03
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908436
   j =  2                              :            45773
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908264
   j =  2                              :            45862
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
 p-value of test no 106                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-5
 p-value of test no 109                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.39
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.54
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.24
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.78
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.58
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.22
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.69
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.76
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.62
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.23
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.93
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.82
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.84
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.01
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.69
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.49
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.94
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.15
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.54
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.04
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.71
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.39
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.13
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.38
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.52
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.60
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.89
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.11
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.28
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.35
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.34
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.11
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.45
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.63
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.72
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.61
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.56
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.91
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.38
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.70
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.48
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.92
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.19
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.98
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 217                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.53
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.91
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.13
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.11
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11438.20
 p-value of test no 229                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.81
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.32
 p-value of test no 231                :  9.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000121180
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.33
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000041557
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    2.09
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.21
 p-value of test no 244                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 246                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:17.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89423885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56748
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5283
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.37
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.69
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.80
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.38
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.84
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.41
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.82
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.88
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.10
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.88
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.58
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.88
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.47
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.55
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907903
   j =  2                              :            46044
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908290
   j =  2                              :            45846
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.043
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.36
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.56
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.19
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.29
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.33
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.86
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.90
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.33
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
 p-value of test no 143                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17040.87
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.89
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.32
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.94
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.17
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.40
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.58
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.30
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.74
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.67
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.46
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.13
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.02
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.48
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.50
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.57
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.11
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.22
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.94
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.08
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.24
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.70
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.81
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.11
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.19
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.60
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.19
 p-value of test no 184                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.33
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.81
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.43
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.30
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.41
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.77
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.54
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.15
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.01
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.62
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.22
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.33
 p-value of test no 231                :    0.9942
 
 
 -----------------------------------------------
 Total number of bits:  8000010627
 
 Normal statistic for number of bits   :   0.084
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.51
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000181348
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:50.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90406925.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56749
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.55
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.04
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.91
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.03
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.71
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.26
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.06
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.26
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.98
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.22
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.17
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.44
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.94
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908704
   j =  2                              :            45645
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46341
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870341
   j =  1                              :        399907321
   j =  2                              :            46335
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.66
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.37
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.34
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.92
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.46
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.62
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.18
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 127                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 128                :  1.0e-2
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.06
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.45
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.51
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17540.24
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.85
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.33
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.98
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.57
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.84
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.53
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.83
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.75
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.19
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.51
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.24
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.88
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.74
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.99
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.27
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.98
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.49
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.14
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.49
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.27
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.13
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.71
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.55
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.40
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.04
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.95
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.37
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.39
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.73
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.64
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10245.44
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.73
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 223                :  9.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    5.64
 p-value of test no 225                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4596.22
 p-value of test no 226                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.24
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.41
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.79
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.91
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.07
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000133756
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.51
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999970547
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 248                :    0.53
 
 Sample variance                       :   0.066
 p-value of test no 249                : 1 -  6.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:42.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91422733.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56750
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5328
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9918
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.72
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.29
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.49
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.09
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.85
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.06
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.37
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.51
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.60
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1332.90
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.78
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.61
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.43
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.80
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  167.91
 p-value of test no 67                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.67
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908217
   j =  2                              :            45881
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908314
   j =  2                              :            45840
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.11
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.97
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.65
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.54
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.73
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.96
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.21
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.83
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.79
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.91
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.41
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.08
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.87
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.23
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.42
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.33
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.12
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.93
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.27
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.39
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.73
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.19
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.64
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.07
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.95
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.75
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.18
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.61
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.15
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.04
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.60
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.12
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.17
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.92
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.87
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.82
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.98
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.10
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10256.62
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.18
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.90
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.70
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.53
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.36
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.07
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.82
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.89
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999928307
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.89
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000056809
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:44.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92471309.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56751
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 7                  :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9947
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.58
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.30
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.08
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.22
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.28
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.26
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.93
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7292.07
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.89
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.37
 p-value of test no 66                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.15
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.84
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908544
   j =  2                              :            45719
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907939
   j =  2                              :            46023
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 92                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.22
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.67
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.82
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.55
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.39
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.06
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.43
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.58
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17800.49
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.25
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.22
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.75
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.93
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.22
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.04
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.05
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.81
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.48
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.66
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.91
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.77
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.62
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.21
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.14
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.30
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.67
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.81
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.71
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.41
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.41
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.30
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.96
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.90
 p-value of test no 175                :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.56
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.50
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.22
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.98
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.81
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.28
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.55
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.98
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.75
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.05
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.53
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.24
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.91
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999961610
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.49
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000023161
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:09.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            9.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93421578.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56752
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997311
   j =  2                              :             1343
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    3.16
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9946
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.44
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.12
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.71
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.37
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.65
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.66
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.81
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1325.22
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.63
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.41
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.46
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.03
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.52
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908310
   j =  2                              :            45839
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908042
   j =  2                              :            45976
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.32
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.39
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.91
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.35
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.93
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.46
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.27
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.17
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.32
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.26
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.66
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.41
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.69
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.56
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.81
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.85
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.98
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.56
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.42
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.13
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.92
 p-value of test no 160                :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.50
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.13
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.11
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.36
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.87
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.37
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.94
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5193.60
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.66
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.11
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.23
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.06
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.88
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.64
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.68
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    2.61
 p-value of test no 184                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.42
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.65
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.15
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.28
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 220                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.97
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.21
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.95
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.92
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.57
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.71
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.93
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999967529
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.11
 p-value of test no 233                :  9.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000306496
 
 Normal statistic for number of bits   :    2.42
 p-value of test no 234                :  7.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 250                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:26.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94437386.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56753
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1246
 p-value of test no 4                  :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334366
   j =  1                              :        599997508
   j =  2                              :             1246
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5670
 p-value of test no 13                 :  4.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.84
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.54
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.10
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.35
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.72
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.31
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.70
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.60
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1320.66
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7360.80
 p-value of test no 57                 :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.53
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.37
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.45
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.96
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45314
 p-value of test no 70                 :    0.9959
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869314
   j =  1                              :        399909375
   j =  2                              :            45308
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908414
   j =  2                              :            45787
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 72                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.53
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.98
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.56
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.95
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.12
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.70
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.56
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.37
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.58
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.34
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.50
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.66
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.70
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.29
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.66
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.95
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.58
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.56
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.44
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.96
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.20
 p-value of test no 157                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.92
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.27
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.93
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.82
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  420.65
 p-value of test no 163                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.19
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.46
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.32
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.07
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.23
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.89
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.01
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.61
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.66
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.90
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.42
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.37
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-3
 p-value of test no 181                :    0.9988
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.82
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.88
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.55
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.35
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.70
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.99
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.80
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3959.85
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.72
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.21
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.83
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.62
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000126778
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.28
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000051160
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.095
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 241                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:44.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            0.9994 
  13  BirthdaySpacings, t = 2         4.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95453194.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56754
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.92
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.84
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.95
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.13
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.55
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.32
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.41
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.10
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.97
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.21
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.77
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.55
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.85
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.17
 p-value of test no 66                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.43
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5195.49
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907983
   j =  2                              :            46004
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 97                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.14
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.36
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.67
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.05
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.56
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.05
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.20
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   68.80
 p-value of test no 129                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.038
 p-value of test no 134                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.66
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17623.09
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.28
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.89
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.60
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.08
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.42
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.10
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.54
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.37
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.35
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.01
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.23
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.35
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.44
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.93
 p-value of test no 162                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.69
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.41
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.66
 p-value of test no 165                :    0.9900
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.52
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.71
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.19
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.02
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.58
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.33
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.76
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.46
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.65
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.16
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 181                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.11
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.42
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.35
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.06
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.45
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.60
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.05
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.13
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4241.17
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.06
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.43
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.76
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999911588
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.56
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999963983
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:58.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96403466.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56755
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5553
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.73
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.89
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.70
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.54
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.84
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.62
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.56
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.32
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  290.04
 p-value of test no 54                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.63
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.98
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.77
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.38
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.76
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.68
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.42
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907756
   j =  2                              :            46116
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908161
   j =  2                              :            45915
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.79
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.46
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.34
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.98
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.16
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.19
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.92
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.83
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17003.75
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.20
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.76
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.12
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.74
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.32
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.67
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.38
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.87
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.22
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.73
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.97
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.15
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.01
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.55
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.84
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.73
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.44
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.49
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.22
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.20
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.85
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.10
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.80
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.42
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.87
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.83
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.38
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.85
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.78
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9691.49
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.34
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.40
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.24
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.57
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.69
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.00
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.60
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000003991
 
 Normal statistic for number of bits   :   0.032
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.52
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999972650
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:11.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97419274.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56756
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     541
 p-value of test no 31                 :    0.9923
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.74
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.57
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.23
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.37
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.75
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.27
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.08
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.99
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.27
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.54
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.34
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.42
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.01
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.18
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.70
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45571
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869571
   j =  1                              :        399908861
   j =  2                              :            45565
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908070
   j =  2                              :            45962
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.7e-3
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  7.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.76
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.74
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.21
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.74
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.42
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.38
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.21
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.14
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.82
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.94
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 144                :  8.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16946.18
 p-value of test no 145                :    0.9955
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.00
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.15
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.05
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.43
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.05
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.46
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.57
 p-value of test no 156                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.83
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.49
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.48
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.42
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.39
 p-value of test no 161                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.45
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.92
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.00
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.29
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.88
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.94
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.76
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.41
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.13
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.69
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.53
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4800.64
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.30
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.36
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.90
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.40
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.33
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.90
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.82
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.39
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5091.59
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.15
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.74
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.03
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.93
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.67
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.12
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000078514
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.63
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999964688
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.44e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:49.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98435082.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56757
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9914
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.40
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.03
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.55
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.58
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.04
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.87
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.07
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.60
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1566.23
 p-value of test no 56                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.17
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.03
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.02
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.98
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.72
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.29
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45558
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908888
   j =  2                              :            45550
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908279
   j =  2                              :            45859
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.84
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.21
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.63
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.08
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.29
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.04
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.73
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.89
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.26
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.80
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.78
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.36
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.85
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.45
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.36
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.55
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.47
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.35
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.25
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.61
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.08
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.50
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.20
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.83
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.03
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.02
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.06
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.49
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.71
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.61
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.84
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.24
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.33
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.10
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 186                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.27
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.96
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.01
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.26
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.33
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 221                :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.87
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.72
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.26
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.08
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.37
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.92
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.00
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000037633
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999845159
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:40.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99483658.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56758
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.46
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.46
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.19
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.75
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.04
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.18
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.50
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.59
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.50
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.81
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.66
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.85
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.22
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.54
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.32
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.93
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907937
   j =  2                              :            46027
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908277
   j =  2                              :            45857
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
 p-value of test no 106                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.52
 p-value of test no 119                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.13
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.26
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.41
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 128                :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.26
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.15
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.26
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.03
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.04
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.68
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.85
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.77
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.00
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.87
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.67
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.70
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.68
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.05
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.30
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.11
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.74
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.60
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.39
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.65
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.45
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.35
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.21
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.07
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.25
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.92
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.91
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.69
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.62
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.32
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.90
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.01
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.13
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.28
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.67
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.49
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.33
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.40
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.95
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.25
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.29
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.92
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000069949
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.77
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999977852
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:57.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100466698.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56759
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7141
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9943
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.73
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.58
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.77
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.57
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.00
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.53
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.86
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.85
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7186.97
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.90
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.95
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.06
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.32
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907839
   j =  2                              :            46073
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908245
   j =  2                              :            45876
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.75
 p-value of test no 116                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.77
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.42
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.12
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.72
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.32
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.18
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.88
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.08
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.22
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17039.91
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.72
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.34
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.67
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.62
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.93
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   66.48
 p-value of test no 151                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.11
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.70
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.90
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.10
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.14
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.85
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.47
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.13
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.16
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.76
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.15
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.74
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.24
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.13
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.25
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.86
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.23
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.32
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.53
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.88
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.98
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.07
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.04
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.48
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-3
 p-value of test no 191                :    0.99
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.88
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.75
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.69
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.00
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.42
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.87
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.61
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.45
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.37
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.44
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.95
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000136138
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.51
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000098560
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:43.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101482506.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56760
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.74
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.46
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.13
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.76
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.46
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.13
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.33
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.24
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.52
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.29
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6819.94
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.87
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.05
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.13
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.16
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.46
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908616
   j =  2                              :            45683
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907795
   j =  2                              :            46095
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.98
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.65
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.67
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.11
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.35
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.09
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 126                :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.96
 p-value of test no 129                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.44
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.37
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.80
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.72
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.50
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.78
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.99
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.96
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.04
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.78
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.10
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.22
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.70
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.48
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.68
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.93
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.15
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.77
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.58
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.11
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.30
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.69
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.68
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.19
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.24
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.87
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.59
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.16
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.85
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.13
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.48
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.87
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.67
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.44
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.68
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.04
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.17
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.53
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.98
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.60
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.91
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.89
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.33
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.51
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.81
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.71
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.28
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000072523
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.69
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000017521
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:39.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82837532.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56761
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7564
 p-value of test no 15                 :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    4.43
 p-value of test no 32                 :  5.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    3.32
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.35
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.26
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.87
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.63
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.31
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.38
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.98
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.27
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.87
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.09
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.19
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.86
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5175.92
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46184
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907635
   j =  2                              :            46178
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908482
   j =  2                              :            45753
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.44
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.64
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.73
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.38
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.77
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.78
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.58
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.50
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.58
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.40
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.22
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.91
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.44
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.77
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.84
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.61
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.21
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.63
 p-value of test no 157                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.20
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.43
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.98
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.26
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.02
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.43
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.47
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.41
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.21
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.57
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.49
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.36
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.25
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.69
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.83
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.02
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.32
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.21
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.30
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.02
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.34
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.48
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.54
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.42
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.00
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4268.69
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.08
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.94
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.04
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000097150
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.22
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999904268
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    2.06
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 250                :  8.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 252                :  3.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.93
 p-value of test no 253                :    0.9983
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:57.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83165199.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56762
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.89
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.15
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.67
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.33
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.50
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.01
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.25
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.10
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.90
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.99
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.47
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.86
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.22
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4924.83
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908490
   j =  2                              :            45746
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908927
   j =  2                              :            45535
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.43e-4
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.29
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.48
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.42
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.08
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.69
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.56
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.71
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.52
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.56
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17181.97
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.59
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.03
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.94
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.39
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.06
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.80
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.96
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.67
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.98
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.37
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.91
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.23
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.29
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.23
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.44
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.13
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.82
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.85
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.88
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.86
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.66
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.00
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.03
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.59
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.28
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.55
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.68
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.63
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.58
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.63
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.72
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.40
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.51
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.50
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.27
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.85
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.96
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 217                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.92
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.72
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.61
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.68
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.90
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.25
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.83
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000109183
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.33
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000062008
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:40.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84148239.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56763
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     660
 p-value of test no 31                 :  8.3e-3
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.35
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.73
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.93
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.76
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  183.32
 p-value of test no 54                 :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.18
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.07
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.35
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.14
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.15
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.10
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.04
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.51
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908635
   j =  2                              :            45675
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908183
   j =  2                              :            45904
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 118                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.51
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.75
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.09
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.75
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.08
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :    9.76
 p-value of test no 125                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.07
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.40
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17297.40
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.15
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.45
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.26
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.86
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.84
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.24
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.59
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.46
 p-value of test no 153                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.20
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.85
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.41
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.81
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.41
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.35
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.31
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.16
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.31
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.44
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.91
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.62
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.30
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.81
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.66
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.75
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.97
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.98
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.77
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.60
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.49
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.52
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.64
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.97
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.08
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.86
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.56
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.73
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3859.44
 p-value of test no 227                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.78
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.66
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12082.17
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.47
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999959306
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.15
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000032713
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.074
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:07.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85229583.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56764
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.15
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.04
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.63
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.92
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.10
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.29
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.56
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.23
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.63
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.37
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.37
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 64                 :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   33.04
 p-value of test no 65                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.67
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.78
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.89
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907842
   j =  2                              :            46070
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908455
   j =  2                              :            45768
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.75
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.68
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.03
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.47
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.35
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.84
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.17
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.76
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.77
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.46
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.76
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.37
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.85
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.03
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.79
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.21
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.70
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.70
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.08
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.32
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.00
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.03
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.47
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.37
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.77
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.17
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.31
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.45
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.45
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.15
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.92
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.70
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.04
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.56
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.30
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.12
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.97
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.43
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.81
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.36
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.41
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.07
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.28
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.06
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.37
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.67
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.43
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.75
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.09
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.18
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.94
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.46
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.58
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999802793
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.51
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999845372
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:37.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86278159.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56765
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     538
 p-value of test no 31                 :    0.9946
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.27
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.19
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.87
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.99
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.95
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.75
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.40
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.26
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.63
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7182.80
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.44
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.06
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.44
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.50
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908372
   j =  2                              :            45808
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908660
   j =  2                              :            45664
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.87
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.59
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.75
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.67
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.10
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.55
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.87
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.40
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.13
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.63
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.72
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.74
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.43
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.22
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.32
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.41
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.91
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.00
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.30
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.16
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.40
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.84
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.57
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.88
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.52
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.46
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.38
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.56
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.53
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.76
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.95
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.98
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.66
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.87
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.74
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.00
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.39
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.59
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.17
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 187                :  5.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 188                :  9.7e-3
 
 Sample variance                       :    4.17
 p-value of test no 189                :  2.1e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.83
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.43
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.49
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.61
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.75
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.33
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.87
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.05
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.36
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.55
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.21
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12144.55
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.73
 p-value of test no 231                :  3.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000217453
 
 Normal statistic for number of bits   :    1.72
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.58
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999819536
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
 p-value of test no 241                :    0.9970
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.35
 p-value of test no 243                :    0.9906
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:43.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87293967.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56766
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.97
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.20
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.49
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.37
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.31
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.60
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.33
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.13
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.40
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.42
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.25
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.03
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.32
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.10
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.55
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.29
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908591
   j =  2                              :            45703
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45568
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869568
   j =  1                              :        399908870
   j =  2                              :            45556
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 73                 :    0.9900
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 76                 :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    7.41
 p-value of test no 78                 :  2.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -4.13e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.46
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.93
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.01
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.44
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.64
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.38
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.88
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.92
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.72
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.18
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17547.66
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.76
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.40
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.80
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.37
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.65
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.98
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.68
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.43
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.85
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.74
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.14
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.96
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.88
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.47
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.47
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.34
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.61
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.07
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.24
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.28
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.69
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.35
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.20
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.79
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.91
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.79
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.73
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.79
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.12
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.02
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 180                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    4.75
 p-value of test no 182                :  4.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.64
 p-value of test no 183                :    0.9959
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.98
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.66
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.32
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.58
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.77
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.77
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.73
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4303.43
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.16
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.71
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.32
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.40
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999945881
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.15
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999974240
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:21.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft AD, t = 8                2.2e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88277007.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56767
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.62
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    3.87
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.71
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.81
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.68
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.66
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.22
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.34
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.41
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.60
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.37
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.72
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.93
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.59
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.76
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908598
   j =  2                              :            45698
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908342
   j =  2                              :            45826
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.98
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.20
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.56
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.73
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.50
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.13
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.78
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.81
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17126.48
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.32
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.93
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.06
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.49
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.40
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.82
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.78
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.50
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.59
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.74
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.81
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.90
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.10
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.59
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.37
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.26
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.83
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.91
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.90
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.20
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.47
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.36
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.27
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.31
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.55
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.22
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.71
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.11
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.94
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 185                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.16
 p-value of test no 189                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.54
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.37
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.23
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.31
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.64
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.89
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.15
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.35
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.49
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11557.24
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.81
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.26
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999922547
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.05
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999942014
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:05.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89194511.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56768
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 12                 :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.10
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.95
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.22
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.98
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.17
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.40
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.96
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.49
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.39
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.88
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.97
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.03
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.40
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.83
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.84
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45531
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869531
   j =  1                              :        399908941
   j =  2                              :            45525
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908096
   j =  2                              :            45943
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 101                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.11
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.35
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.68
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.00
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.78
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.59
 p-value of test no 124                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.10
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.05
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.78
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.76
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.96
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.80
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.44
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.42
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.15
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.77
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.37
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.81
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.62
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.05
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.44
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.01
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.06
 p-value of test no 160                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.72
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.25
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.66
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.62
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.97
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.46
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.26
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.17
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.48
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.54
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.71
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.25
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.21
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.07
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.25
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.48
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.37
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.21
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.51
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.57
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.92
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.75
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.13
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.62
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4272.02
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.91
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.81
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.07
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999970439
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.01
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999969248
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:42.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90210319.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56769
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4213
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.15
 p-value of test no 35                 :  2.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.44
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.05
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   22.81
 p-value of test no 53                 : 1 -  5.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.20
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.24
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.75
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6852.28
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.87
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.6e-3
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 64                 :  4.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.33
 p-value of test no 65                 :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.35
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.95
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.77
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908308
   j =  2                              :            45840
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908035
   j =  2                              :            45978
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 85                 :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 108                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.31
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.62
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.49
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.92
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.82
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.66
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.69
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.49
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.50
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.48
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17795.47
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.31
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.60
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.80
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.24
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.78
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.06
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.73
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.80
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.17
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.10
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.87
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.10
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.73
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.51
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.62
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  463.80
 p-value of test no 167                :  3.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5205.26
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.14
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.64
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.51
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.52
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.68
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.91
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.19
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.40
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.56
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.05
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.64
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.19
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.39
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10247.51
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.56
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.22
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.38
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.05
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.41
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.80
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.02
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.72
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000003751
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999942506
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9921
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 243                :    0.05
 
 Sample variance                       :    2.00
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:23.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  33  CouponCollector, r = 27        1 -  5.9e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91226127.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56770
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.00
 p-value of test no 49                 :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.63
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.36
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.80
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.61
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.44
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.40
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.18
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.26
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.32
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.14
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.39
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.38
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908122
   j =  2                              :            45939
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907976
   j =  2                              :            46003
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.86
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.69
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.77
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.79
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.93
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 131                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.04
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.10
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.23
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.20
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.33
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.87
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.30
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.06
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.31
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.79
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.03
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.44
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.48
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.20
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.70
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.65
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.71
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.96
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.63
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.31
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.83
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.65
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.20
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.09
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.67
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.92
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.08
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.25
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.36
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.83
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.05
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.68
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.02
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.02
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.19
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.25
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.51
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.94
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.00
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.30
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.26
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12179.37
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.57
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.94
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999918056
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.75
 p-value of test no 233                :  8.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000170974
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:18.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92241935.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56771
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 11                 :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.50
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.85
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.42
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.60
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.03
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.74
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.66
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.89
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7186.23
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.00
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.80
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.66
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  157.38
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.07
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908143
   j =  2                              :            45924
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908487
   j =  2                              :            45752
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.66e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.35
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.36
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.81
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.40
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.70
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.86
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.83
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.18
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.57
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17608.32
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.57
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.31
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.14
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.02
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.15
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.26
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.74
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.30
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.13
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.33
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.77
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.72
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.70
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.97
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.20
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.28
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.28
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.85
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.57
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.02
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.75
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.01
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.97
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  312.11
 p-value of test no 174                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.43
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.06
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.82
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 181                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    7.35
 p-value of test no 182                :  2.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.42
 p-value of test no 183                :  3.2e-4    *****
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.48
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.79
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.03
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.80
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10293.77
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.44
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.63
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.87
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.05
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.13
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.76
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.54
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.84
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999784886
 
 Normal statistic for number of bits   :   -1.70
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.24
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000090760
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:59.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  82  LempelZiv, r = 0                3.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93224975.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56772
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    5.57
 p-value of test no 32                 :  1.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.33
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.13
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.64
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.42
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.02
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.34
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.88
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.02
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6846.98
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.21
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.57
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.63
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.53
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4868.72
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908510
   j =  2                              :            45742
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908068
   j =  2                              :            45963
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 106                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.36
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.89
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.22
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.90
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.35
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.04
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.49
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17603.39
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.46
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.02
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.87
 p-value of test no 148                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.58
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.09
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.34
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.39
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.79
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.71
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.37
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.42
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.77
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.42
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.26
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.46
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.72
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.77
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.91
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.46
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.90
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.00
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.64
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  263.26
 p-value of test no 170                :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.06
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.71
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.25
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.42
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.33
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.53
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.57
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.98
 p-value of test no 196                :    0.9984
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.35
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.29
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9722.20
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 212                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9707.94
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.32
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.60
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.63
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.73
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.23
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.11
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.57
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000153064
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.53
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000077575
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:07.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94273551.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56773
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 12                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9939
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.06
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.89
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.19
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.03
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.75
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.61
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.56
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.82
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.89
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.33
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.37
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.98
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.62
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.83
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.74
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908577
   j =  2                              :            45707
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907964
   j =  2                              :            46015
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.09
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.72
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.83
 p-value of test no 121                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.05
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.66
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.70
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.64
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.78
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17756.73
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.19
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.92
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.22
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.83
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.54
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.90
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.30
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.05
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.32
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.69
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.69
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.91
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.11
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.96
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.27
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.38
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.34
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.71
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.79
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.19
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.33
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.17
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.26
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.33
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.45
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5212.60
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.20
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.90
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.17
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.15
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.35
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.81
 p-value of test no 198                :  5.3e-3
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 201                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.46
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.52
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.04
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10267.75
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.58
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.40
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.82
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.92
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.32
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.02
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.41
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999898328
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.53
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999922346
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:57.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95289359.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56774
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 32                 :    0.9987
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.56
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.70
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.63
 p-value of test no 48                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.36
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.62
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.23
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.57
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1265.07
 p-value of test no 56                 :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.30
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.21
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.39
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.13
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.36
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.29
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46226
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870226
   j =  1                              :        399907552
   j =  2                              :            46218
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908171
   j =  2                              :            45907
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.57
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.13
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.63
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.60
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.79
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.74
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.00
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.03
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.99
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.38
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.85
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.81
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.09
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.25
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.64
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.09
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.40
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.52
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.42
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.46
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.16
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.51
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.47
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.50
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.17
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.45
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  417.98
 p-value of test no 163                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.72
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.11
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.21
 p-value of test no 166                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.34
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.09
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.81
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.20
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.63
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.81
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.47
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.01
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.70
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.01
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.54
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.79
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.11
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.99
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.48
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.15
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.05
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.84
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.48
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.76
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.06
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.13
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.75
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000138586
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.85
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999972578
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.068
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:47.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96239631.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56775
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.42
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.85
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.09
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.84
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.47
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.11
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.88
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.90
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.35
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.53
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7297.05
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.48
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.10
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.23
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.86
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908022
   j =  2                              :            45983
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908218
   j =  2                              :            45885
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.58
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.52
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.12
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.91
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.78
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.13
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.97
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.89
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.42
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.90
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.96
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.23
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.24
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.13
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.05
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.28
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.44
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.83
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  201.54
 p-value of test no 157                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.95
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.77
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.36
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.57
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.31
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.86
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.66
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.87
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.98
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.50
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.22
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.32
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.50
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.62
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.90
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.40
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.84
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.90
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.43
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.32
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.08
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.14
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10242.35
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.22
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.12
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.07
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.52
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.96
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.54
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.65
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.05
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999980474
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.05
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999955739
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:40.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97255439.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56776
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7068
 p-value of test no 21                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     834
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.42
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.12
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.94
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.91
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.54
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.10
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.93
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.38
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.46
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.84
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.66
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.74
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.01
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46209
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870209
   j =  1                              :        399907585
   j =  2                              :            46203
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908192
   j =  2                              :            45895
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9913
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.75
 p-value of test no 115                :  8.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.98
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.57
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.79
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.46
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.67
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   56.61
 p-value of test no 125                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.40
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.76
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.68
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 142                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17817.86
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.59
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.11
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.68
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.13
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.20
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.64
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.01
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.45
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.09
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.36
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.61
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.85
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.93
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.42
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.63
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.94
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.97
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.53
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.31
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.09
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.71
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.18
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.58
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.05
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.45
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.73
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.09
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.51
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.35
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.69
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.21
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.37
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9748.19
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.34
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.79
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.55
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.22
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.17
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.76
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.37
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.66
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000019756
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.90
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000036346
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    2.14
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:20.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  55  SampleCorr, k = 1               8.9e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98271247.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56777
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 12                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5644
 p-value of test no 13                 :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    4.62
 p-value of test no 27                 :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.65
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.53
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.06
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.72
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.96
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.42
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.46
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.33
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.61
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.43
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.09
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.64
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.69
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.33
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.15
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907995
   j =  2                              :            45995
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908325
   j =  2                              :            45830
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.67
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.83
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.38
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.62
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.90
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.47
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.56
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 130                :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.10
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.36
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17706.90
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.28
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.27
 p-value of test no 147                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.15
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.57
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.25
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.71
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.40
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.61
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.14
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.25
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.94
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.12
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.82
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.51
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.50
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.25
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.17
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.61
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.31
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.75
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5232.13
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.34
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.32
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.01
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.52
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.77
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.93
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.06
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.49
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.08
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    2.25
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 202                :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.80
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.95
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9873.49
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 213                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.83
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.45
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.72
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.39
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3917.39
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.97
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.48
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.42
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999968294
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.98
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000075337
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.074
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.14
 p-value of test no 254                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:21.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99287055.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56778
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    4.05
 p-value of test no 38                 :  8.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.40
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.70
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.54
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.55
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.94
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  173.22
 p-value of test no 54                 :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.89
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.80
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.40
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.84
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.81
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.00
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.74
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.21
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907662
   j =  2                              :            46166
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45480
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909044
   j =  2                              :            45472
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 103                :  7.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 105                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.26
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.68
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.43
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.34
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.88
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.54
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.41
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.39
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17686.00
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.46
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.03
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.19
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.10
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.24
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.29
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.66
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.80
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.64
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.43
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.54
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.11
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.44
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.73
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.76
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.02
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.04
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.58
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.13
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.12
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.31
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.96
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.40
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.47
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.24
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.72
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.58
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.24
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.79
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.82
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.41
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.57
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.95
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.28
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.86
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.04
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.07
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.40
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.11
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.14
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.18
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999843599
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.52
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999905939
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:58.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100302863.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56779
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.40
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.38
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.03
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.41
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.88
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.00
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6872.04
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.21
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.60
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.38
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.46
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5146.69
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908098
   j =  2                              :            45945
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46242
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870242
   j =  1                              :        399907518
   j =  2                              :            46238
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.37e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.84
 p-value of test no 115                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.68
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.01
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.38
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.25
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.79
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.40
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.31
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.78
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.19
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.84
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.36
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.39
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.94
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.10
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.58
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.04
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.69
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.56
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.31
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.63
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.12
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.11
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.27
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.71
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.45
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  114.59
 p-value of test no 165                :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.24
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.86
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.84
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.91
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.43
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.01
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.90
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.63
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.06
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.20
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.24
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.00
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.17
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.82
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.18
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.47
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
 p-value of test no 219                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.36
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.47
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.89
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.35
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.39
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12219.78
 p-value of test no 230                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.73
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999971321
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999829889
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:18.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101318671.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56780
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 11                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.11
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     543
 p-value of test no 31                 :    0.9903
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.57
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.26
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.04
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.62
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.42
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.43
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.15
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.53
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.17
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6846.78
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.51
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.66
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.01
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.19
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908342
   j =  2                              :            45829
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908749
   j =  2                              :            45621
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 114                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.89
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.04
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.82
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.99
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.68
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.51
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.02
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.76
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.03
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.23
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.29
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.30
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.25
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.82
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.88
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.89
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.52
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.41
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.27
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.69
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.14
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.04
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.54
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.78
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.83
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.48
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.25
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.05
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.02
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.25
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.30
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.18
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.47
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.42
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.81
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.50
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.67
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.55
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.31
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.37
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.54
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.44
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.45
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.61
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.10
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.86
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3940.92
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.51
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.45
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.44
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.21
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000095218
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.73
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000003574
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 251                :    0.9906
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:25.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82870301.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56781
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7533
 p-value of test no 18                 :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    3.50
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.24
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.98
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.70
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.31
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.67
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.99
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.18
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.95
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.24
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.42
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.59
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.33
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.00
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908026
   j =  2                              :            45984
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908084
   j =  2                              :            45955
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 78                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.60
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.02
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.79
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.91
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.17
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.90
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.74
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.89
 p-value of test no 137                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.51
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.62
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.99
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.58
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.94
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.19
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.51
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.43
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.93
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.38
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.73
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.94
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.38
 p-value of test no 158                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.75
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.26
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.47
 p-value of test no 161                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.65
 p-value of test no 162                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.95
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.86
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.05
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.16
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.23
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.28
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.51
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.41
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.69
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.84
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.66
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  472.04
 p-value of test no 174                :  7.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.72
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.71
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.10
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.57
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 201                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.39
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 205                :    0.9922
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 206                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  144.60
 p-value of test no 207                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.79
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.40
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.83
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.67
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.84
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.75
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.92
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.87
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.40
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999967229
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.04
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000018859
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.26
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:08.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   7.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83591197.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56782
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7103
 p-value of test no 20                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.66
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.81
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.28
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.20
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.83
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.29
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.01
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.97
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.11
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.85
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.70
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.09
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908226
   j =  2                              :            45881
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908398
   j =  2                              :            45792
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.47
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.74
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.27
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.49
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.23
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.02
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.76
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.88
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.51
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.81
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.06
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.87
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.40
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.54
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.51
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.05
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.32
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.52
 p-value of test no 154                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.12
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.23
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.22
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  595.17
 p-value of test no 158                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.07
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.13
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.68
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.87
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.10
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.86
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.71
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.63
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.45
 p-value of test no 167                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.48
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.71
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.81
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.49
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.64
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.83
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.67
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.57
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.44
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.55
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.62
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.64
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.14
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.53
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.91
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.10
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.67
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.05
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.22
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.61
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000109345
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.83
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000127051
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:44.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84639773.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56783
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.66
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.99
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.51
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.96
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.09
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.84
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.11
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.61
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 63                 :    0.9943
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.53
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.00
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.03
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908095
   j =  2                              :            45945
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908711
   j =  2                              :            45643
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.63e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.06
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.81
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.40
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.69
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.46
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.53
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.34
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.83
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.41
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.67
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.84
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.10
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.91
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.55
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.97
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.48
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.90
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.69
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.01
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.90
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.58
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.04
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.13
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.43
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.18
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.57
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.17
 p-value of test no 165                :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.25
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.62
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.09
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.08
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.89
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.35
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.78
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.80
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.19
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.16
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.12
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.00
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-4
 p-value of test no 190                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.80
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.35
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.66
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.59
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.98
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.02
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.09
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.86
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.73
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.54
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.40
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.33
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999875327
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.27
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000139060
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.029
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:31.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85753885.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56784
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    5.73
 p-value of test no 42                 :  1.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.62
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.24
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.15
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.83
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.32
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.80
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.35
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.20
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.24
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.78
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.27
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.68
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.16
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.41
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908514
   j =  2                              :            45734
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908557
   j =  2                              :            45717
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.55
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.82
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.46
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.93
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.64
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.85
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 127                :    0.9948
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.71
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.60
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.20
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.00
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.83
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.90
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.32
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.88
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.12
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.13
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.08
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.52
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.83
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.39
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.62
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.42
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.56
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.46
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.57
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.78
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.05
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.04
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.11
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.47
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.22
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.75
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.25
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.45
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.12
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.06
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.63
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.49
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.83
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.72
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.11
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.64
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.31
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.38
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.76
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.35
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.05
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.69
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.40
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.50
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.06
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.49
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999947753
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.43
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000115612
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -2.82e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:31.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86736925.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56785
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7498
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    4.77
 p-value of test no 42                 :  3.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.04
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.75
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.57
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.43
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.98
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.64
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.99
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.25
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.80
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.14
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.18
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.71
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.16
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.82
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.39
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4857.54
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908017
   j =  2                              :            45987
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907791
   j =  2                              :            46100
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.95
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.69
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.50
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.74
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.34
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.33
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.09
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
 p-value of test no 131                :    0.9958
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.35
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.72
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.41
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.30
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.56
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.10
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.79
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.70
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.54
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.99
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.05
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.32
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.28
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.11
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.03
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.11
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.93
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.83
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.59
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.49
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.10
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.78
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.47
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.71
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.50
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.56
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  144.52
 p-value of test no 170                :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.33
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.60
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.15
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.78
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.58
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.23
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    2.33
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.57
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.65
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.71
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.24
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.12
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.00
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.97
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4306.11
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.17
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.14
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.98
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000135208
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.94
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000022738
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:45.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87719965.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56786
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.48
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.60
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.82
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.22
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.71
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.21
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.77
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.46
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.30
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.89
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.92
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.26
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.34
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.00
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.33
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908603
   j =  2                              :            45697
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46259
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870259
   j =  1                              :        399907488
   j =  2                              :            46247
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 86                 :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.74
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.81
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.69
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.32
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.87
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.94
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.08
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.07
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.75
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17495.00
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.95
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.28
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.89
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.27
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.11
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.72
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.91
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.70
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.39
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.72
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.34
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.87
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.49
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.54
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.38
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.38
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.65
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.16
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.75
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.62
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.80
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.96
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  446.24
 p-value of test no 169                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.21
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.79
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  297.42
 p-value of test no 172                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.82
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.45
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.36
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.33
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.97
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.41
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.14
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.02
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.86
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.87
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.69
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.93
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.87
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.94
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.57
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.99
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999799442
 
 Normal statistic for number of bits   :   -1.59
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.95
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000035299
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 243                :    0.9936
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 247                :  8.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 248                :    0.9974
 
 Sample variance                       :    2.41
 p-value of test no 249                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:31.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88670237.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56787
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 5                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.08
 p-value of test no 23                 :  8.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.24
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.53
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.25
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.07
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.89
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.00
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.35
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.98
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.85
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.25
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6776.89
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.38
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.70
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.20
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.38
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.62
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908294
   j =  2                              :            45844
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908755
   j =  2                              :            45615
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.65
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.04
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.62
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.21
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.65
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.77
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.97
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.06
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.88
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.25
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.92
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.17
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.93
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.59
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.17
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.68
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.15
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.00
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.14
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.81
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.56
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.77
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.24
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.96
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.49
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.34
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.81
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.95
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.69
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.07
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.54
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.64
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.72
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.58
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.11
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.27
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.03
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.22
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.08
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.70
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.48
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.62
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 206                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.37
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9716.49
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.87
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.72
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.88
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.90
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.43
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11490.47
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.28
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.03
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000034924
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.57
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999991691
 
 Normal statistic for number of bits   :  -0.066
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:37.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89686045.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56788
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.93
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.40
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   86.48
 p-value of test no 51                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.78
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.29
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.62
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.78
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.54
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.74
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.00
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.74
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.83
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.65
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4852.04
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908016
   j =  2                              :            45986
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908380
   j =  2                              :            45807
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.95
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.85
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.17
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.02
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.80
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.29
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.06
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.02
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.22
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17198.42
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.89
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.56
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.26
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.45
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.03
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.15
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.88
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.60
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.24
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.11
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.40
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.97
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.48
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.27
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.52
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.02
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.56
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.50
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.51
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.71
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.85
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.04
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.32
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.84
 p-value of test no 171                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.91
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.09
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.33
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.10
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.21
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.77
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.75
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.97
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.89
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
 p-value of test no 220                :    0.9954
 
 Anderson-Darling statistic = A2       :    6.07
 p-value of test no 221                :  9.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4559.09
 p-value of test no 222                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.75
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.78
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.88
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.75
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.09
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.36
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999902732
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.41
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999815423
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:02.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  95  HammingIndep, L=30, r=0         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90669085.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56789
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9911
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 45                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.90
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.92
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.05
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.78
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.01
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.06
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.76
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.78
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.72
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.00
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.44
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908241
   j =  2                              :            45875
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907792
   j =  2                              :            46101
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.08
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.54
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.34
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.79
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.67
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.41
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.53
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.44
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.90
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.91
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.94
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.39
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.01
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.84
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.05
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.06
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.24
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.39
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.04
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.00
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.14
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.78
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.22
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.84
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.74
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.10
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.49
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.62
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.66
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.81
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.16
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.51
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.13
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.23
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.45
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.35
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.79
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.06
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.09
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.74
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.68
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.56
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.77
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.14
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.94
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10375.27
 p-value of test no 211                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.24
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.67
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.19
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.61
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.13
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.87
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11564.31
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.32
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000030955
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.42
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999929633
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:47.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91652125.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56790
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    3.93
 p-value of test no 27                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    3.52
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.70
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.37
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.62
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.85
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.23
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.66
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.38
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.21
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.37
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.03
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.88
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.11
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908542
   j =  2                              :            45723
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45358
 p-value of test no 71                 :    0.9926
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869358
   j =  1                              :        399909287
   j =  2                              :            45352
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 107                :    0.9950
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.08
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.59
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.29
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.15
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.01
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.19
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.74
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.42
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.85
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.91
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.85
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.55
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.26
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.29
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.07
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.43
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.37
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.30
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  207.87
 p-value of test no 156                :  5.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.02
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.04
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.76
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.69
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.30
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.78
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.54
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.52
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.56
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.48
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.71
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.24
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.43
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.27
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.55
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.50
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.22
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.50
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.90
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.83
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.60
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.64
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.33
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.10
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.06
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.17
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.00
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.74
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.67
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.46
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000017233
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.43
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999973307
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
 p-value of test no 241                :    0.9985
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.86
 p-value of test no 243                :    0.9979
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:59.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     5.9e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92799005.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56791
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5539
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.77
 p-value of test no 22                 :  3.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.64
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.48
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.03
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.65
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.61
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.28
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.37
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.97
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.82
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.50
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.96
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.76
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.12
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908741
   j =  2                              :            45622
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46391
 p-value of test no 71                 :  8.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870391
   j =  1                              :        399907224
   j =  2                              :            46379
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.11
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.47
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.83
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.26
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.42
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.54
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.15
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.50
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.24
 p-value of test no 135                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.62
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.32
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.86
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.75
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.56
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.10
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.96
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.77
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.32
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.07
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.10
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.80
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.54
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.15
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.31
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.75
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.41
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.41
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.36
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.47
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.04
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.74
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.16
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.70
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.53
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.49
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.22
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.63
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.98
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.44
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.19
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.00
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.61
 p-value of test no 176                :  8.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.78
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.24
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.58
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.16
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.60
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.78
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.37
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.38
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.49
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.82
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.94
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.20
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.63
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.06
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999913442
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.82
 p-value of test no 233                :  3.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000052540
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:24.21
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93782045.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56792
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.20
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.56
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.23
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.55
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.26
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.27
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.61
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.90
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.45
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1348.10
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.54
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.12
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.21
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.56
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.94
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908310
   j =  2                              :            45836
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46237
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870237
   j =  1                              :        399907528
   j =  2                              :            46233
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
 p-value of test no 84                 :    0.9930
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.66
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.16
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.27
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.34
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.53
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.88
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.93
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.78
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.01
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.99
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.45
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.62
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.96
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.85
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.04
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.62
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.23
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.04
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.85
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.07
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.43
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.18
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.18
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.36
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.21
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.67
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.66
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.81
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.49
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.47
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.33
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.19
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.21
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.16
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.90
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.76
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.32
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.04
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.61
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.33
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.59
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.19
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.45
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10217.29
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.13
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.99e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.67
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.57
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3923.13
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.26
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.61
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.83
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.29
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000012583
 
 Normal statistic for number of bits   :   0.099
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000023941
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    2.98
 p-value of test no 249                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:10.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94863389.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56793
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.40
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.98
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.07
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.80
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.34
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.11
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.76
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.98
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.37
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.76
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.43
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.61
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5252.62
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908407
   j =  2                              :            45792
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908540
   j =  2                              :            45721
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.95
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.69
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.90
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.50
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.81
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.22
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.31
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.45
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.25
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.02
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.62
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.68
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.42
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.71
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.02
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.48
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.33
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.80
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.00
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.95
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.76
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.65
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.16
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.83
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.13
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.05
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  600.20
 p-value of test no 163                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.79
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.26
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.81
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.91
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.03
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.83
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.30
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.92
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.05
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4765.97
 p-value of test no 173                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.87
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.04
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.73
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    2.60
 p-value of test no 189                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.02
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.40
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.89
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.60
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10269.57
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.32
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.08
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.82
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.84
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.81
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.26
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999994061
 
 Normal statistic for number of bits   :  -0.047
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.33
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999915263
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:22.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95780893.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56794
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.13
 p-value of test no 22                 :    0.9995    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     256
 p-value of test no 37                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.90
 p-value of test no 39                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.59
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.74
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.51
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.21
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.43
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.85
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.11
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.46
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.21
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.86
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.13
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.06
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.24
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46304
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870304
   j =  1                              :        399907401
   j =  2                              :            46286
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907950
   j =  2                              :            46022
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.85
 p-value of test no 119                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.96
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.08
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.48
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.17
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.11
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.33
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.77
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.32
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.67
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 143                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 144                :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17932.53
 p-value of test no 145                :  3.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.36
 p-value of test no 146                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   14.80
 p-value of test no 147                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.68
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.10
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.95
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.13
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.23
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.79
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.90
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.15
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.36
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.48
 p-value of test no 158                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.32
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.41
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.71
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.23
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.24
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.94
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.30
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.02
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.14
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.53
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.23
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.13
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.42
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.02
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.92
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.29
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.00
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.46
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.30
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.67
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.73
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.10
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.39
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.61
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.72
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.87
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.17
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.47
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.66
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.53
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.37
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000109123
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.53
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000013780
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.90
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:59.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96731165.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56795
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.75
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.39
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.77
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.01
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.98
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.20
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.42
 p-value of test no 52                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.08
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.06
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.52
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.73
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.27
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.59
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.67
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908220
   j =  2                              :            45887
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46227
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870227
   j =  1                              :        399907547
   j =  2                              :            46225
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-6
 p-value of test no 113                :    0.9966
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.48
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.32
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.16
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.88
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.95
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.40
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.39
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.78
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.30
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.96
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 138                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.63
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17529.76
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.57
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.88
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.31
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.65
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.66
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.87
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.88
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.93
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.13
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.34
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.31
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.75
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.97
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.53
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.48
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.34
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.11
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.13
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.59
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  443.86
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.26
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.32
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.08
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.65
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.45
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.97
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.04
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.56
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.30
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.98
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.40
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.84
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.45
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.70
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.33
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.98
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.89
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.31
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000181192
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.64
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999999899
 
 Normal statistic for number of bits   : -7.98e-4
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:57.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97779741.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56796
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.01
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.04
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.24
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.95
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.19
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.80
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.94
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.60
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.99
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.39
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.91
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.09
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45681
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869681
   j =  1                              :        399908641
   j =  2                              :            45675
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45564
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869564
   j =  1                              :        399908877
   j =  2                              :            45554
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.29
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.23
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.02
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.91
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.22
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.24
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.04
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.19
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.65
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.61
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.86
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.24
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.35
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.66
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.64
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.88
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.25
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.15
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.39
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.77
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.12
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.19
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.43
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.38
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.50
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.21
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.41
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.18
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.85
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.37
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.58
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5277.28
 p-value of test no 168                :  3.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.62
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.85
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.71
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.72
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.60
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.52
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.17
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.35
 p-value of test no 176                :  9.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.99
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.14
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.31
 p-value of test no 198                :    0.9955
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.88
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.74
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.20
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.97
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.53
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.73
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.17
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.91
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.62
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.00
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.70
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000054094
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.26
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000102250
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.036
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:18.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98664477.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56797
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9955
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.65
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.50
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.26
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.93
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.89
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.30
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.61
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.48
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.38
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.27
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6882.97
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.71
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.09
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.50
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.78
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908138
   j =  2                              :            45925
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908058
   j =  2                              :            45965
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-4
 p-value of test no 112                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 114                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.47
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.69
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.80
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.18
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.81
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.43
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.12
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.89
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.68
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17231.03
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.13
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.44
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.50
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.05
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.84
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.93
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.17
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.10
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.81
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.85
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.38
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.24
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.72
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.51
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.55
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.93
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.04
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.47
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.59
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.46
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.77
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.74
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.63
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.64
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.58
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.79
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.60
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.97
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.23
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.85
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.86
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.18
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.36
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.64
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.51
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.63
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.17
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.28
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.33
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.00
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.33
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.36
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.85
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000061969
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.12
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000047284
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:42.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99680285.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56798
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7516
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    3.50
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.97
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.28
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.14
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.11
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.39
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.24
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.21
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  358.03
 p-value of test no 55                 :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.83
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.95
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.00
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.76
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.88
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.51
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.68
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908391
   j =  2                              :            45803
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908052
   j =  2                              :            45971
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.06
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.53
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.07
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.94
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.91
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.75
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.92
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.06
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.80
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.65
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.39
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.71
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.97
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.56
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.67
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.48
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.88
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.94
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.64
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.08
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.29
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.38
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.69
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.87
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.53
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.32
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.25
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.27
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.28
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.52
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.20
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.39
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.00
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.84
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.14
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.04
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.05
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.00
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.75
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.38
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.77
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.22
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.15
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.74
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.40
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.45
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.02
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.62
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.61
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.86
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999932243
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.77
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000067813
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -8.04e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.54
 p-value of test no 253                :    0.9945
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:16.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100925469.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56799
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9924
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.79
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.06
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.68
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.12
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.83
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.71
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.68
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  363.73
 p-value of test no 55                 :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.61
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.64
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.03
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.13
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.23
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.37
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908347
   j =  2                              :            45819
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908448
   j =  2                              :            45764
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 86                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 97                 :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 99                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.78
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.17
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.87
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.94
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.91
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.69
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.29
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.02
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.28
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.75
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.09
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.13
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.93
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.01
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.21
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.58
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.81
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.40
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.54
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.21
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.06
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.10
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.21
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.02
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.64
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.97
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.13
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.88
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.66
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.50
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.29
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.96
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.32
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.96
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.95
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.45
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.57
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.36
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.02
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.39
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.67
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.15
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.74
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.33
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.01
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.94
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.73
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.91
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.35
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.42
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.26
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.95
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999965303
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.34
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999902039
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
 p-value of test no 251                :    0.9952
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:46.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101908509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56800
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     343
 p-value of test no 37                 :  8.0e-3
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.36
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.77
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.30
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.19
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.02
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.78
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.53
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  505.25
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.97
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.83
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.58
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.32
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.20
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.40
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908650
   j =  2                              :            45672
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46433
 p-value of test no 71                 :  5.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870433
   j =  1                              :        399907137
   j =  2                              :            46427
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.59
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.25
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.87
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.93
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.10
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.29
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.59
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.20
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.99
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.85
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.85
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.02
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.26
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.58
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.39
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.15
 p-value of test no 153                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.63
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.00
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.28
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.21
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.76
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.75
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.72
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.18
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.39
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.96
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.75
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.38
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.57
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.43
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5216.97
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.61
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.59
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.59
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.22
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.80
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.25
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.50
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.19
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.41
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.50
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.66
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.98
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.23
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.63
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.14
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4317.61
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.52
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.57
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11465.50
 p-value of test no 230                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.90
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999844268
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000040306
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:31.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82903070.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56801
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.98
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.72
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.20
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.92
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.26
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.27
 p-value of test no 53                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.40
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.40
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.04
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.95
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.38
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.09
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.35
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.89
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.88
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908122
   j =  2                              :            45930
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 100                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.47
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.11
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.73
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.45
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.93
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.90
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.88
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.77
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.39
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.31
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.91
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.28
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.10
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.10
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.96
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.19
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.10
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.69
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.17
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.65
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.07
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.52
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.30
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.25
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.42
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.78
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.72
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.12
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.50
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.53
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.25
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.96
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.18
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.26
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.57
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.28
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.32
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.29
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.02
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.64
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9935
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.81
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.75
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.16
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.82
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.94
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.17
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.14
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.81
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.13
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.34
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.07
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000102637
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.59
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000097990
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:52.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83034142.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56802
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.02
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.22
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.47
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.89
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.56
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.07
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.03
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.35
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6869.78
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.37
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.59
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.59
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.44
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.69
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45626
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869626
   j =  1                              :        399908748
   j =  2                              :            45626
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908107
   j =  2                              :            45939
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.44
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.17
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.58
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.60
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.90
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.20
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.09
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.36
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.21
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 139                :    0.9937
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.34
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17341.90
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.55
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.14
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.54
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.48
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.46
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.96
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.62
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.51
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.50
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.12
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.66
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.39
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.96
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.21
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.14
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.51
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.79
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.38
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.80
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.89
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.43
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.98
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.08
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.89
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.67
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.27
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.69
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.06
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.74
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    2.08
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.57
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.52
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.60
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.19
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
 p-value of test no 219                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5145.06
 p-value of test no 222                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.06
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.11
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.77
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.02
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.54
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.08
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000055528
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.93
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999993413
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:26.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83951646.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56803
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.72
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.04
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.44
 p-value of test no 47                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.14
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.99
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.13
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.45
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.36
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.41
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.39
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.00
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4731.30
 p-value of test no 68                 :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908329
   j =  2                              :            45825
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908530
   j =  2                              :            45729
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 97                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.63
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.16
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.94
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.62
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.50
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.99
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.69
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.77
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.68
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17755.87
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.05
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.83
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.49
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.55
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.97
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.48
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.43
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.83
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.08
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.94
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.41
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.63
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.90
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.58
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.14
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.59
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.77
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.50
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.80
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.75
 p-value of test no 170                :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.50
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.33
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.62
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.86
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.91
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 200                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 202                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.73
 p-value of test no 203                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.75
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.58
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.13
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-4
 p-value of test no 219                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5144.11
 p-value of test no 222                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.01
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.57
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.76
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.82
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.11
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.31
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000144451
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.10
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000081064
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.086
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:40.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              0.9991 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84967454.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56804
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.36
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.90
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.25
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.70
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.12
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.21
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.98
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1536.73
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.17
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.52
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.56
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.51
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.83
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907678
   j =  2                              :            46158
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908140
   j =  2                              :            45930
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.09
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.40
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.79
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.69
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.49
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.36
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.89
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.50
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.39
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.07
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.38
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.05
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.93
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.43
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.16
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.77
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.39
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.37
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.50
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.27
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.00
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.97
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.34
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.58
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.86
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.05
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.37
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.74
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.29
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.51
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.52
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.48
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.59
 p-value of test no 171                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.56
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.24
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.85
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.95
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.67
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.28
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.40
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.28
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 220                :    0.9927
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4677.99
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.51
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.33
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.29
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.50
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.42
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.72
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000083203
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.47
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999975893
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:42.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86016030.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56805
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     538
 p-value of test no 31                 :    0.9946
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.06
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.38
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.64
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.25
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.72
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.99
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.43
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.70
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.28
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1296.53
 p-value of test no 56                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.04
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.27
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.08
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.27
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.35
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46270
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870270
   j =  1                              :        399907463
   j =  2                              :            46264
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908316
   j =  2                              :            45839
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.97
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.87
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.55
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.31
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.15
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.23
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.38
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.60
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.73
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.34
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.40
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.28
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.35
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.94
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.35
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.51
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.71
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.35
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.19
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.26
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.07
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.37
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.54
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.42
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.74
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.69
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.94
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.42
 p-value of test no 167                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.50
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  447.66
 p-value of test no 169                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.04
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.04
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.31
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.89
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.38
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.84
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.53
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.00
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.92
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.80
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.44
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.82
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.20
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.03
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.41
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.04
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.70
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.34
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.01
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.41
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000040321
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.74
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000064804
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:38.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86999070.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56806
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.38
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.75
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.70
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.84
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.00
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.15
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.98
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.49
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.06
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.10
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9916
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.63
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.67
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   83.46
 p-value of test no 67                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.28
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45558
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908885
   j =  2                              :            45556
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45544
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869544
   j =  1                              :        399908914
   j =  2                              :            45540
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.93
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.62
 p-value of test no 120                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   36.28
 p-value of test no 121                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.02
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.67
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.49
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.26
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.56
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.56
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.56
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.97
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.00
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.12
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.69
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.47
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.40
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.85
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.97
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.83
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.21
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.73
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.58
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.08
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.21
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.06
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.36
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.60
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.76
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.10
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.71
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.55
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.11
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.09
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.21
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.95
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.65
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.60
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.79
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.97
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.26
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.47
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.77
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.77
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.47
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.41
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.00
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.94
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.63
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.85
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.21
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.30
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.63
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.29
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.82
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000031246
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.89
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000081070
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:37.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  61  WeightDistrib, r = 28           0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88014878.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56807
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.28
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.79
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.14
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.27
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.35
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.91
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.24
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.53
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.87
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.41
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.48
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.66
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.21
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.54
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.59
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.24
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.60
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45407
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869407
   j =  1                              :        399909188
   j =  2                              :            45403
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46065
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907876
   j =  2                              :            46053
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.78
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.69
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.22
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.35
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.16
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.45
 p-value of test no 125                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.10
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.94
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.65
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.90
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.85
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.10
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.07
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.37
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.16
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.31
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.30
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.42
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.88
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.49
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.77
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.39
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.40
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.05
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.19
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.67
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.28
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.61
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.23
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.25
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.90
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.79
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.69
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.85
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.97
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  299.30
 p-value of test no 172                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.88
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.49
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.88
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.80
 p-value of test no 176                :  5.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.11
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.46
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.47
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.86
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.23
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.55
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.16
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.05
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.11
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.78
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4321.29
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.44
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.55
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.92
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000024208
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.61
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999969230
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:21.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89030686.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56808
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.04
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.24
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.24
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.32
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.60
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.66
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.58
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.30
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.22
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.70
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.12
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.71
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5226.80
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45432
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869432
   j =  1                              :        399909139
   j =  2                              :            45426
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907960
   j =  2                              :            46011
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 98                 :    0.9915
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.27
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.56
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.68
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.35
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.99
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.45
 p-value of test no 129                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    5.26
 p-value of test no 132                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.32
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.32
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.77
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17648.68
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.75
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.65
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.80
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.11
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.49
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.97
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.75
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.65
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.90
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.46
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.31
 p-value of test no 159                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.90
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.71
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.13
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.89
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.58
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.12
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.14
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.83
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.37
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.02
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.90
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.10
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.07
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.56
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.56
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.20
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.32
 p-value of test no 198                :  9.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.21
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.81
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 209                :    0.9915
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9683.44
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.30
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.22
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.54
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.81
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.69
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.52
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.38
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.30
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000073789
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.90
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000209104
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    2.13
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:10.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90046494.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56809
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1486
 p-value of test no 4                  :  6.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334606
   j =  1                              :        599997028
   j =  2                              :             1486
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    5.26
 p-value of test no 45                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.24
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.11
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.30
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.62
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.76
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.89
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.59
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.19
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.23
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.46
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.44
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.67
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5255.91
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907851
   j =  2                              :            46067
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908095
   j =  2                              :            45948
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-4
 p-value of test no 80                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 115                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.02
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.67
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.10
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.53
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.27
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.42
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.60
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.20
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.36
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.10
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.75
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.78
 p-value of test no 149                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.82
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.98
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.01
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.97
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.35
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.88
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.90
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.11
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.67
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.10
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.35
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.37
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.79
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.46
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.36
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.41
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.52
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.73
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.98
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.72
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.01
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.20
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5217.00
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.19
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.11
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.62
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.14
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.08
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 182                :  6.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.73
 p-value of test no 183                :  3.1e-3
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.40
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.33
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.29
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.22
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9719.71
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.12
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.53
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.84
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.93
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.78
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.88
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.03
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999819005
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.99
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000192178
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:05.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            6.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91062302.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56810
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 4                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9954
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.54
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.38
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.58
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.50
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.68
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.01
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.45
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.12
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.19
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.39
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.21
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.51
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.41
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.10
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908319
   j =  2                              :            45836
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907699
   j =  2                              :            46143
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.49
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.34
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.56
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.51
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.34
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.20
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.44
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.66
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.36
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.30
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.41
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.45
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.14
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.65
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.96
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.05
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.22
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.13
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.49
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.14
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.02
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.37
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.32
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.69
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.54
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.33
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.89
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.21
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.84
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.73
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.65
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.80
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.63
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.01
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.42
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.64
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.01
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.41
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.08
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.28
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.26
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.19
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.02
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.42
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.90
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.20
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4275.59
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.45
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.74
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.64
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999977201
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.57
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000044260
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 237                :  5.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.76
 p-value of test no 238                :  2.9e-3
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9914
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:35.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92078110.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56811
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4174
 p-value of test no 14                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    7.24
 p-value of test no 39                 :  2.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.20
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.32
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.19
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.75
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.09
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.40
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.59
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.39
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.66
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.12
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.04
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.16
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.16
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45426
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869426
   j =  1                              :        399909152
   j =  2                              :            45418
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908426
   j =  2                              :            45784
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9943
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.11
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.69
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.45
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.45
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.85
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.56
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.60
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.73
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.63
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 143                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17141.28
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.40
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.12
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.37
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.88
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.37
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.45
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.45
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.34
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.39
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.87
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.82
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.88
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.25
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.86
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.68
 p-value of test no 161                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.60
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.58
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.21
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.75
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.33
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.80
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.14
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.45
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.42
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.24
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.91
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.09
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.07
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.56
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.93
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.22
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.23
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.68
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.32
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.39
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.43
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.52
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.36
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.54
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11639.40
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.33
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.22
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999885902
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.24
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999998933
 
 Normal statistic for number of bits   : -8.44e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 248                :    0.9933
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:10.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2S, t = 9         2.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93093918.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56812
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4199
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    2.80
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.58
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.77
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.96
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.49
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.92
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.26
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.31
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.20
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.08
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.69
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.20
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.15
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.95
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.38
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908643
   j =  2                              :            45668
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908432
   j =  2                              :            45772
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.13
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.62
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.83
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.83
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.11
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.76
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.06
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.96
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.85
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.93
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.08
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.30
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.86
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.26
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.75
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.42
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.95
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.34
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.98
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.81
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.09
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.57
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.61
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.23
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.31
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.96
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  308.13
 p-value of test no 167                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.21
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.47
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.18
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.39
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.93
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.89
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.62
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.75
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.99
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.91
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.10
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.08
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.57
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.01
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.89
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.73
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.73
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.53
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12212.33
 p-value of test no 229                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11571.34
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.91
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999890093
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.42
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999898949
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:07.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94109726.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56813
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  5.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5535
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.17
 p-value of test no 28                 :  2.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.57
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.18
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.65
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.72
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.27
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.32
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6890.64
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.85
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.20
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.48
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.78
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4767.33
 p-value of test no 68                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908559
   j =  2                              :            45716
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908301
   j =  2                              :            45839
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.23
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.06
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.05
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.08
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.12
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.42
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.33
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.17
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.12
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.04
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17020.08
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.43
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.61
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.44
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.64
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.98
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.56
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.92
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.41
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.39
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.47
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.46
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.03
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.32
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.94
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.24
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.23
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.95
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.30
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.31
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.82
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.04
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.34
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.70
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.25
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.66
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.48
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.39
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.28
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.62
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.16
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.51
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.33
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.09
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.06
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.29
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.26
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.36
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.98
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.09
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.48
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.40
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.09
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.17
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999959492
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.88
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000020998
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:13.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95125534.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56814
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5265
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.46
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.82
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.08
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.22
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.10
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.97
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.17
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.33
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6954.84
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.71
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.98
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.74
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.78
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45361
 p-value of test no 70                 :    0.9923
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869361
   j =  1                              :        399909281
   j =  2                              :            45355
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908132
   j =  2                              :            45931
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 94                 :    0.9938
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.40
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.25
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.82
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.57
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.60
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.97
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.57
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.78
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.28
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17575.72
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.76
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.24
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.08
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.82
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.86
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.27
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.55
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.52
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.48
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.18
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.62
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.10
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.41
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.30
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.87
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.84
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.92
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.58
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.10
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.21
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.54
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.86
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.69
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.95
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.35
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.82
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.72
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.42
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.06
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.20
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.15
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.83
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.18
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.91
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.19
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.92
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.32
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.12
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3937.12
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.24
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.54
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.90
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.08
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000065914
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.78
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999951455
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:00.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96141342.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56815
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7071
 p-value of test no 15                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.63
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 39                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.53
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.19
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.24
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.12
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.45
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.14
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1315.18
 p-value of test no 56                 :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.52
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.73
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.72
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.05
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.14
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.23
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46161
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870161
   j =  1                              :        399907680
   j =  2                              :            46157
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908049
   j =  2                              :            45968
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.07
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.01
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.67
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.38
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.54
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.87
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.49
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.75
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.91
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.79
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17112.79
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.27
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.59
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.83
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.43
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.17
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.21
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.99
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.66
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.56
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.08
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.48
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.53
 p-value of test no 161                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.50
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.15
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.28
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.11
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.09
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.19
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.02
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.70
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.29
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.50
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.97
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.39
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.65
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.12
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.63
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.95
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.29
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.10
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.20
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 214                :  8.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9647.54
 p-value of test no 215                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.84
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.14
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.54
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4303.05
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.38
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12121.20
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000121951
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.78
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000119995
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
 p-value of test no 235                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    3.41
 p-value of test no 254                :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:17.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97157150.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56816
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.53
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.27
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.44
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.36
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.39
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.29
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.49
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.81
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.28
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.77
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.36
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.40
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.84
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.96
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908516
   j =  2                              :            45736
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908304
   j =  2                              :            45842
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.02
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.95
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.44
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.84
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.96
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.77
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.32
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.29
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.77
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.60
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 139                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.51
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.49
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.95
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.84
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.59
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.53
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.82
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.86
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.45
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.67
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.27
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.83
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.30
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.88
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.23
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.78
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.12
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.00
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.44
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.77
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.43
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.69
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.75
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.41
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.20
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.13
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.76
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.03
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.05
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.46
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.29
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 193                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.66
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.29
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.04
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.74
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.41
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10261.80
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.60
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.64
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3957.95
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.08
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.18
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.17
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.43
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000016003
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.18
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000030499
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:34:48.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98172958.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56817
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997207
   j =  2                              :             1395
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    3.12
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.13
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.89
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.02
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.72
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.84
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.94
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.22
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.85
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.11
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.94
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.17
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-3
 p-value of test no 63                 :    0.9985
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.71
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.71
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.70
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46157
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870157
   j =  1                              :        399907692
   j =  2                              :            46145
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45340
 p-value of test no 71                 :    0.9941
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869340
   j =  1                              :        399909325
   j =  2                              :            45330
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.22
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.29
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.52
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.82
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.25
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.05
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.01
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.17
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17724.39
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.33
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.01
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.22
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.29
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.73
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.77
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.08
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.42
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.65
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.27
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.86
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  422.60
 p-value of test no 158                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.89
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.60
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.32
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.16
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.34
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.02
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.27
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.71
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.05
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.28
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.66
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.21
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.82
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.44
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4781.47
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.82
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.93
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.32
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.13
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.51
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.48
 p-value of test no 198                :    0.9931
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.61
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.14
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.82
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.11
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.06
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.57
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.69
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.00
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.03
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.74
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.10
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999998801
 
 Normal statistic for number of bits   : -9.48e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.13
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000033586
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.058
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:14.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99188766.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56818
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.44
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.02
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.27
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.90
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.68
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.44
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.24
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.94
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.13
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.70
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45580
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869580
   j =  1                              :        399908843
   j =  2                              :            45574
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908169
   j =  2                              :            45914
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.26
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.08
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.94
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.66
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.85
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.49
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.87
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.81
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.86
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.52
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.17
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.28
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.40
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.84
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.73
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.63
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.51
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.76
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.26
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.32
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.45
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.28
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.00
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.03
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.35
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.83
 p-value of test no 162                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.16
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.63
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.07
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.68
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.92
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.60
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.11
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.32
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.48
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.81
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.24
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.67
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.76
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.02
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.81
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.96
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.31
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.45
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.49
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.68
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.60
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.87
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.37
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.21
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.69
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.06
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.61
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000003547
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.07
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000080965
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.078
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:55.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100204574.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56819
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.05
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    3.55
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.26
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.17
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.93
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.08
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.18
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.86
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.33
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.46
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.74
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.62
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.03
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.71
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.71
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.23
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908311
   j =  2                              :            45837
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908137
   j =  2                              :            45924
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.01
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.46
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.31
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.67
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.99
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.55
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.25
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.42
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.04
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.70
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.48
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.81
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.42
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.36
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.55
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.34
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.34
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.81
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.46
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.50
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.59
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.84
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.99
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.97
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.17
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.98
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.08
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.31
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.07
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.33
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.70
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.00
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.09
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.37
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.25
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.36
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.48
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.49
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.28
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.37
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.14
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.32
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.17
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.27
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.11
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.66
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11528.31
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.99
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.42
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999760427
 
 Normal statistic for number of bits   :   -1.89
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.20
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999990311
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
 p-value of test no 250                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:35:26.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101220382.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56820
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.13
 p-value of test no 22                 :  2.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.60
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.60
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.69
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.77
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.53
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.11
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.09
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.76
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7259.87
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.98
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.30
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.31
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.23
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908558
   j =  2                              :            45718
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907811
   j =  2                              :            46087
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.61
 p-value of test no 115                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.19
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.02
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.28
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.53
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.26
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.69
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.54
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.83
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.24
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16982.96
 p-value of test no 145                :    0.9921
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.33
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.22
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.11
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.58
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.58
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.24
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.55
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.89
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.39
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.30
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.49
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.57
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.28
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.60
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.41
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.08
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.99
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.22
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.48
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.02
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.84
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.64
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.78
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.65
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.94
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  308.58
 p-value of test no 171                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.11
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.30
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.64
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.39
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.74
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.49
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.56
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.03
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.93
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-4
 p-value of test no 220                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4652.05
 p-value of test no 222                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.27
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.67
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.04
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.25
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.38
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.34
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000013138
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.15
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000062821
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.45
 p-value of test no 243                :  7.1e-3
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:02.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 81920000.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56821
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.76
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    4.75
 p-value of test no 44                 :  3.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.84
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.45
 p-value of test no 49                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.05
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.60
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.55
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.78
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.28
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.30
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.55
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.30
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.43
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.24
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.01
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.51
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45443
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869443
   j =  1                              :        399909116
   j =  2                              :            45439
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46087
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870087
   j =  1                              :        399907829
   j =  2                              :            46081
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 85                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -1.48e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.09
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.13
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.92
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.24
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.06
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.74
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.65
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.93
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.27
 p-value of test no 137                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.47
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17253.92
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.01
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.98
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.41
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.28
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.64
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.35
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.23
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.78
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.67
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.79
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.41
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.42
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.96
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.32
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.49
 p-value of test no 165                :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.67
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.58
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.60
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.33
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.92
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.34
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.34
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.48
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.36
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.20
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.00
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.87
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.44
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.33
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.90
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.86
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.35
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.43
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.47
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.63
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.70
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.99
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.40
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.21
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.79
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000034963
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.28
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000117664
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:13.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83558400.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56822
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 10                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4185
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    4.25
 p-value of test no 26                 :  6.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    2.97
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.25
 p-value of test no 34                 :  6.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9966
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.32
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.97
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.00
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.76
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.68
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.48
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.71
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.82
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.34
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7312.55
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.92
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.72
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.90
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.23
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.52
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907946
   j =  2                              :            46021
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908496
   j =  2                              :            45740
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.16
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.65
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.11
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.03
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.79
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.33
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.87
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.81
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.16
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.00
 p-value of test no 147                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.39
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.84
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.68
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.79
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.53
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.53
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.94
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.65
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.09
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.71
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.27
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.48
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.39
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.85
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.95
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.06
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.35
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.25
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.10
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.62
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.61
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.87
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.15
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.75
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.68
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.63
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.57
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.44
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.91
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.55
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.01
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.25
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.90
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.19
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.07
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.41
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.15
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.48
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999801272
 
 Normal statistic for number of bits   :   -1.57
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.78
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000041728
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.013
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:34.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84312079.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56823
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 4                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 11                 :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.13
 p-value of test no 23                 :    0.9997    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.62
 p-value of test no 47                 :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.21
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.28
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.33
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.79
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.87
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.05
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.62
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.68
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.45
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.51
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.61
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.28
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.34
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.73
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.25
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908409
   j =  2                              :            45791
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908389
   j =  2                              :            45804
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.52
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.13
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.56
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.98
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.98
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.27
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.74
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.47
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.91
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.12
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.40
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17356.16
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.17
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.69
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.76
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.11
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.78
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.72
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.88
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.29
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.55
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.29
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.94
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.64
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.82
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.84
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.10
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.07
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.29
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.73
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.92
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.07
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.74
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.12
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.40
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.61
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.60
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.08
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.86
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.13
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.01
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.82
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.04
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.48
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.18
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.09
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.20
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.34
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.19
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.25
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.82
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999958976
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.99
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000045298
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:05.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9990 
  22  ClosePairs mNP, t = 3           0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85622799.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56824
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.47
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.82
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.63
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.13
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.50
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.39
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6890.26
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.40
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.72
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.62
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.91
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.08
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908778
   j =  2                              :            45605
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908092
   j =  2                              :            45948
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.28
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.45
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.18
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.53
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.84
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.89
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.95
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.64
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.92
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.35
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.31
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.45
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.02
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.38
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.65
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.86
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.45
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.29
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.35
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.80
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.47
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.51
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.27
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.93
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.49
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.50
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.63
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   95.20
 p-value of test no 164                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.08
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.77
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.03
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.28
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.30
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.53
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.09
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.46
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.95
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.66
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.24
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.00
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.01
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.04
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.95
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.16
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.85
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.76
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.00
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.84
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.98
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.32
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.74
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.54
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999863057
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.54
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999980207
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:32.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86441999.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56825
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.79
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.90
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.45
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.98
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.56
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.40
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.41
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.93
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.13
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.15
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.28
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.62
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.55
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.64
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907769
   j =  2                              :            46111
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907523
   j =  2                              :            46234
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
 p-value of test no 83                 :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-3
 p-value of test no 101                :    0.9971
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.25
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.05
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.34
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.08
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.78
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.26
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.50
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.48
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.79
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.47
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.10
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.93
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.96
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.42
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.86
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.25
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.23
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.25
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.21
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.35
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.11
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.10
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.22
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.61
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.87
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.29
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.49
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.26
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.40
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.50
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4750.63
 p-value of test no 168                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.11
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.17
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.56
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.32
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.37
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.44
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.95
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.70
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.42
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.99
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.35
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.87
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.90
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.31
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.00
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.41
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4333.57
 p-value of test no 228                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.68
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.82
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.96
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999995333
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.89
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000048745
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:27.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87326735.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56826
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    2.80
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.93
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.38
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.23
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.52
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.52
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.48
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.51
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.16
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.78
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.26
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.60
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.98
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.04
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.04
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5250.66
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908641
   j =  2                              :            45678
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.25
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.67
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.63
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.89
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.29
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.48
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.65
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.90
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.21
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.064
 p-value of test no 135                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
 p-value of test no 138                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.78
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17510.67
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.58
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.18
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.53
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.74
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.33
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.93
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.31
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.25
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.59
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.62
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.89
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.67
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.80
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.81
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.28
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.24
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.40
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.14
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.13
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.56
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.85
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.10
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.53
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.90
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.15
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.69
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.64
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.66
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.76
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.33
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.05
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.88
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.67
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9736.59
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.88
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.79
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.98
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.96
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.50
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.63
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.17
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.41
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999854597
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.98
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000000694
 
 Normal statistic for number of bits   : 5.49e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9932
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:52:31.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88440847.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56827
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 11                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4521
 p-value of test no 16                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4192
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.02
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     968
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.64
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.61
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.62
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.49
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.33
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.73
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.83
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.40
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.61
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.84
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7232.12
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.19
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.28
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.76
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.61
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.88
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46382
 p-value of test no 70                 :  9.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870382
   j =  1                              :        399907239
   j =  2                              :            46376
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908281
   j =  2                              :            45855
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.36
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.95
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.95
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.69
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.85
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.00
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.91
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 144                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17468.52
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.26
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.93
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.13
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.29
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.48
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.26
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.98
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.57
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.80
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.16
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.46
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.26
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.33
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.03
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.96
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.82
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.46
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.21
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.17
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.85
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.72
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.29
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.67
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.65
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.45
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.79
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.80
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.76
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.32
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.18
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.69
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.64
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.07
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.06
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.95
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.37
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.45
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000162298
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.43
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999870500
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:55.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90013711.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56828
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7112
 p-value of test no 20                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7579
 p-value of test no 21                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.30
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.75
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.49
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.86
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.23
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.01
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.12
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.84
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.72
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.50
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.11
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.99
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.98
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908432
   j =  2                              :            45784
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908380
   j =  2                              :            45804
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 78                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    5.74
 p-value of test no 108                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-4
 p-value of test no 113                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.75
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.47
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.57
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.85
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.23
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.08
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.36
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.92
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.26
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.80
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.05
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.68
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.75
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.53
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.92
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.79
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.87
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.13
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.81
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.57
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.86
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.53
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.63
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.05
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.56
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.95
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.85
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.98
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.86
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.73
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.09
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.16
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.99
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.40
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.57
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.28
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.33
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.61
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.91
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.40
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.11
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.60
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.47
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.05
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.91
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.73
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.48
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.66
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.51
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.81
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.96
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11571.71
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.03
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000071992
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.76
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999890213
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    2.44
 p-value of test no 244                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:32.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90996751.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56829
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997271
   j =  2                              :             1363
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 8                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    4.54
 p-value of test no 38                 :  4.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.69
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.52
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.72
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.92
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.60
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.76
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.56
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.15
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.58
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.50
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.84
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.52
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45526
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908950
   j =  2                              :            45522
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908531
   j =  2                              :            45724
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-5
 p-value of test no 112                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 114                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.66
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.21
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.86
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.50
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.21
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.44
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.73
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  174.50
 p-value of test no 141                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.71
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.58
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.68
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.25
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.80
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.99
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.65
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.44
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.28
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.60
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.50
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.18
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.03
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.89
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.72
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.43
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.84
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.12
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.08
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.30
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.47
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.32
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.16
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.29
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.82
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.38
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.13
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.62
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.96
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.72
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.42
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.83
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.84
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.67
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.74
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10235.86
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.08
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.72
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.97
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.96
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.56
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.75
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.49
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.59
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999969056
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.51
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999896876
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -4.26e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:40.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91914255.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56830
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 12                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.85
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.89
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.89
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.80
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.18
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.15
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.83
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7322.73
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.25
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.88
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.99
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.80
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908329
   j =  2                              :            45828
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45535
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869535
   j =  1                              :        399908930
   j =  2                              :            45535
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.21
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.47
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.21
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.37
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.76
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.60
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.67
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.00
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.18
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.38
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17139.75
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.82
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.21
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.37
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.21
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.23
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.31
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.29
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.66
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   56.01
 p-value of test no 154                :  2.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.10
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.80
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.83
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.82
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.15
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.24
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.47
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.08
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.65
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.33
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.73
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.08
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.17
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.48
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.07
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.46
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.39
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.44
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.20
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.93
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.18
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.10
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    2.26
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.52
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.53
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.76
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.52
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.84
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.48
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.13
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.13
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.39
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.23
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.41
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.06
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000105244
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999934100
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:28.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      2.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92930063.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56831
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4491
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.46
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.79
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.98
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.38
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   92.49
 p-value of test no 52                 :  8.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.34
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.69
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.99
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.13
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.06
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.91
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.50
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.72
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.41
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.79
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46157
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870157
   j =  1                              :        399907688
   j =  2                              :            46153
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908469
   j =  2                              :            45764
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 72                 :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  4.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 86                 :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 7.09e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.05
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.12
 p-value of test no 121                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.76
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.83
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.82
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.17
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.38
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.02
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.15
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.41
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.06
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.05
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.37
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.82
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.52
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.25
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.97
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.58
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.75
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.64
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.95
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.18
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.14
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.38
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.10
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.74
 p-value of test no 162                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.33
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.82
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.52
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.93
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.32
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.09
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.41
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.44
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.79
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.52
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.82
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.16
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.09
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.87
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.01
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.62
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.57
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.36
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.46
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.37
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.34
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5046.76
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.38
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.22
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.65
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.83
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.92
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999982802
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.89
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000228994
 
 Normal statistic for number of bits   :    1.81
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:10.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         8.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93913103.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56832
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7542
 p-value of test no 20                 :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 27                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.62
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.64
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.27
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.56
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.23
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.33
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.53
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.30
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.79
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.78
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.48
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.84
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.46
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.95
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908622
   j =  2                              :            45683
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908526
   j =  2                              :            45734
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.48
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.28
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.42
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.75
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.73
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.63
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.51
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.20
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17641.88
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.92
 p-value of test no 146                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.59
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.79
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.23
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.69
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.38
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.82
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.11
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.80
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   99.13
 p-value of test no 157                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.02
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.94
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.41
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.66
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.78
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.65
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.55
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.81
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.03
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.93
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.13
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.73
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.42
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.06
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.71
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.35
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.59
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.73
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.73
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.35
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.99
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.79
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.25
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.59
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.06
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.32
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 212                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9717.19
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.11
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.99
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.59
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.43
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.43
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.63
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.89
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999989354
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.78
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999987251
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.074
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:03.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94863375.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56833
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 6                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.50
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.05
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.82
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.85
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.17
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.48
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.59
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7273.92
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.20
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.21
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.78
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.53
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5180.92
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907983
   j =  2                              :            45998
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45534
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869534
   j =  1                              :        399908938
   j =  2                              :            45522
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 79                 :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 84                 :    0.9932
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.86
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.95
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.44
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.07
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.57
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.97
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.16
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.99
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.18
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.63
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.73
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.81
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.39
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.57
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.83
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.95
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.52
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.61
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.04
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.58
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.29
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.45
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.27
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.29
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.59
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.57
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.04
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.13
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.18
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.18
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.48
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.53
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.58
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.70
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.02
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.04
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.72
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-4
 p-value of test no 209                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9659.75
 p-value of test no 211                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.57
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.74
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.67
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.63
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.43
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.77
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.39
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.62
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999896468
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.28
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000075112
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9964
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:57.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95846415.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56834
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4159
 p-value of test no 14                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.45
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.54
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.09
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.88
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.08
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.98
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.44
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1272.71
 p-value of test no 56                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.75
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.73
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.65
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.97
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.98
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.57
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908815
   j =  2                              :            45582
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908169
   j =  2                              :            45908
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 99                 :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.80
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.47
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.93
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.74
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.41
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.08
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.99
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.58
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17532.82
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.60
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.55
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.65
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.04
 p-value of test no 151                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.46
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.53
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.49
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.86
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.06
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.63
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.66
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.13
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.90
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.37
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.16
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.62
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.79
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.51
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.16
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4711.05
 p-value of test no 168                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.31
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.46
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.62
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.95
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.86
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.39
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.94
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.11
 p-value of test no 196                :  9.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.67
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.60
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.32
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.70
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.69
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.92
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.40
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.27
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.82
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.62
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.16
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000014830
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.68
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000014020
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.23
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 250                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 253                :    0.9901
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:56.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96862223.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56835
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9970
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.61
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.79
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.29
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.01
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.36
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.72
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.12
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.81
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.54
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.19
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.98
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.84
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.00
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.79
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.59
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46359
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870359
   j =  1                              :        399907286
   j =  2                              :            46351
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907818
   j =  2                              :            46082
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.42
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.99
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.21
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.97
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.25
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.29
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.05
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.82
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.92
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.21
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.98
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.58
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.57
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.82
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.49
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.83
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.21
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.67
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.20
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.33
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.78
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.10
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.30
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.76
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.07
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.77
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.59
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.12
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.72
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.91
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.25
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.09
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.05
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.38
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.76
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.73
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.87
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.12
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.43
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.25
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.89
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.18
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.79
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.86
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.28
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.07
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.17
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.58
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11512.44
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.01
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.96
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000047323
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.25
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000045964
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.80e-4
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:48.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97878031.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56836
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9916
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     666
 p-value of test no 31                 :  4.2e-3
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9928
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.58
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.72
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.97
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.67
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.97
 p-value of test no 53                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.82
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.88
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.61
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.79
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.44
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.76
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.25
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.22
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908260
   j =  2                              :            45864
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45597
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869597
   j =  1                              :        399908810
   j =  2                              :            45589
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 92                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-5
 p-value of test no 110                :    0.9952
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.78
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.85
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.20
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.74
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.54
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.05
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.21
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.00
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.98
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.23
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.02
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.02
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.59
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.70
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.57
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.33
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.64
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.07
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.49
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.19
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.20
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.61
 p-value of test no 155                :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.84
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.19
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.30
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.48
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.99
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.12
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.08
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.91
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.04
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.44
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.80
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.01
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.97
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.40
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.74
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.37
 p-value of test no 171                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.86
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.85
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.78
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.85
 p-value of test no 175                :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.19
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.95
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.71
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.60
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.84
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.47
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.01
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.99
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.72
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.05
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.43
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.85
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4319.48
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.17
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.76
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.11
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000049366
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000137329
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:05.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98893839.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56837
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.15
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.80
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.21
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.80
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.37
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.24
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7114.62
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.33
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.52
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.93
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.33
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.34
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908277
   j =  2                              :            45860
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
 p-value of test no 104                :    0.9989
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 105                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.66
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.68
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.40
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.19
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.20
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.92
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.16
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.60
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.85
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.08
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.33
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.45
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.50
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.32
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.76
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.61
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.69
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.09
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.71
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.77
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.71
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.40
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.49
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.39
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.68
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.12
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.04
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.58
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.61
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.60
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.04
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.95
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.72
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.41
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.01
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.64
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.26
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.94
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.57
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.28
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.19
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.30
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.00
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.52
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4374.44
 p-value of test no 227                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.74
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.66
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.63
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.25
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000068098
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.23
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999832433
 
 Normal statistic for number of bits   :   -1.32
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:30.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99909647.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56838
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 10                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 11                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5301
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4193
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.09
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.47
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.86
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.65
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.00
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.74
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.67
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.95
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.78
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.00
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.60
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.64
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.44
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.15
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.58
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908031
   j =  2                              :            45980
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908508
   j =  2                              :            45740
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-3
 p-value of test no 79                 :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
 p-value of test no 104                :    0.9982
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 106                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.34
 p-value of test no 117                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.54
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.51
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.94
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.97
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.99
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.28
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.98
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.83
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.64
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.53
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17369.59
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.85
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.93
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.43
 p-value of test no 149                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.23
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.46
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.55
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.77
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.48
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.08
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.18
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.53
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.35
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.96
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.76
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.81
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.80
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.76
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.79
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.05
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.80
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.27
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.64
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.22
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.20
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.56
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.68
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.04
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.39
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.24
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 181                :    0.9968
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    2.05
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.29
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.07
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.88
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10284.25
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9795.91
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.75
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.76
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.95
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.16
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.92
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.30
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.73
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999949679
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000025399
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:05.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100827151.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56839
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5610
 p-value of test no 13                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.97
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    4.18
 p-value of test no 45                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.21
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.22
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.30
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.58
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.11
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.59
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.21
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.11
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.98
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.41
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.76
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.23
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.17
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.88
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.67
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.64
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907960
   j =  2                              :            46014
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45698
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869698
   j =  1                              :        399908611
   j =  2                              :            45684
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-4
 p-value of test no 109                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.83
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.02
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.76
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.53
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.16
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.83
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.69
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.14
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.13
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.61
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.78
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.15
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17262.84
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.29
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.00
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.81
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.68
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.08
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.20
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.32
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.76
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.20
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.87
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.24
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.74
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.41
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.24
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.26
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.05
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.63
 p-value of test no 165                :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.60
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.14
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.05
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.03
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.25
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.70
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.37
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.90
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.01
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.44
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.55
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.60
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.89
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.44
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.67
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.76
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.46e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5042.90
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.14
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.71
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.78
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.14
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.20
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.52
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999895331
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.10
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000054754
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:21.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101810191.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56840
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.52
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.04
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.25
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.56
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.90
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.66
 p-value of test no 52                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.97
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.04
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.63
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.35
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.75
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.36
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.49
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.07
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.19
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.59
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46185
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907634
   j =  2                              :            46177
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908443
   j =  2                              :            45771
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.01e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.12
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.58
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.16
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.91
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.07
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.95
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.22
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.05
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.63
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.01
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.71
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.67
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.76
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.08
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.59
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.29
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.02
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.01
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.40
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.32
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.22
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.22
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.30
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.95
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.97
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.83
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.58
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.12
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.87
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.27
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.26
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.46
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.95
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.97
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.08
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.40
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.01
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.38
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.13
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.23
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.86
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.77
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12085.84
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.47
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.60
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000030130
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.76
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000044614
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 251                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:02.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 81952769.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56841
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    4.49
 p-value of test no 32                 :  5.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.38
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.55
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.16
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.90
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.60
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.27
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.66
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.10
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.23
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.73
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6929.50
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.15
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.30
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.22
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.90
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5285.18
 p-value of test no 68                 :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46297
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870297
   j =  1                              :        399907409
   j =  2                              :            46291
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908525
   j =  2                              :            45730
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
 p-value of test no 94                 :    0.9975
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.37
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.56
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.23
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.19
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.78
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.75
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.97
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.25
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.03
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17269.72
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.69
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.42
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.82
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.95
 p-value of test no 150                :    0.9935
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.78
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.37
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.03
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.03
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.80
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.81
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.41
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.01
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.76
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.02
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.51
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.76
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.68
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.25
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.73
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.95
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.86
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.75
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.37
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.63
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.22
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.95
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.46
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.36
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.61
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.65
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.76
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.27
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.65
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.04
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.81
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.45
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.37
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.91
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000153910
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.60
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999966203
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:36.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83001361.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56842
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.61
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.06
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.34
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.74
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.91
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.56
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7056.76
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.48
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.16
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.03
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.31
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907744
   j =  2                              :            46122
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908502
   j =  2                              :            45740
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.25
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.50
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.34
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.16
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.22
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.11
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.12
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.40
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.47
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17189.07
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.20
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.68
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.17
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.67
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.63
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.20
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.53
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.11
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.42
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.27
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.05
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.31
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.49
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.40
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.80
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.91
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.50
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.83
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.23
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.75
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.30
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.22
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.82
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.86
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.54
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.14
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.04
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.85
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.12
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.79
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.09
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.42
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.23
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 224                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    5.06
 p-value of test no 225                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5184.64
 p-value of test no 226                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.12
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.24
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.65
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.48
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.02
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000027265
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.70
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000074809
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 252                :    0.9995    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:20.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84115473.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56843
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.87
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.86
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.28
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.96
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.48
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.81
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.33
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.17
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.45
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.79
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.93
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.91
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.71
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908117
   j =  2                              :            45937
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908327
   j =  2                              :            45829
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.19
 p-value of test no 116                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.02
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.87
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.26
 p-value of test no 121                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.23
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.10
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.05
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.66
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17708.94
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.60
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.09
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.84
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.99
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.37
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.40
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.89
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.96
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.68
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.29
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.91
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.92
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.09
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.65
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.14
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.59
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.35
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.24
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.46
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.13
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.70
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.90
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.88
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.25
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.42
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.17
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4778.25
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.24
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.67
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.13
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.26
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.25
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.60
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.99
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.21
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.21
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.29
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.53
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.79
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4244.06
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12060.29
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.32
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.05
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999953903
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.40
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999977225
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.077
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:36.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85065745.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56844
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.09
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.69
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.99
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.94
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.18
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.59
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.30
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.54
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.86
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.98
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7153.86
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.65
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.79
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.53
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.06
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.89
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908929
   j =  2                              :            45531
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908624
   j =  2                              :            45673
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 94                 :    0.9959
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.54
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.96
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.35
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.30
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.84
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.74
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.90
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.65
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.85
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.10
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.28
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.71
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.67
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.30
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.81
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.79
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.14
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.95
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.08
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.33
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.14
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.23
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.31
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.82
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.67
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.02
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.69
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.11
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.31
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.10
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.29
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.85
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.92
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.73
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.27
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.41
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.26
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.63
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.22
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.10
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.07
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.34
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.44
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.00
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.55
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.45
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.52
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.64
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.73
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.86
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.10
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.55
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.13
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000028699
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.11
 p-value of test no 233                :  4.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999976556
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 235                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:11.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86179857.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56845
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 12                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     673
 p-value of test no 31                 :  1.8e-3
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 41                 :    0.9971
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.70
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.35
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.97
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.86
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.26
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.54
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.20
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.95
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.90
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.37
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908402
   j =  2                              :            45793
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907810
   j =  2                              :            46089
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.78
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.55
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.50
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.93
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.15
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.81
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.28
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.85
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.75
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.72
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.65
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.21
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.38
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.25
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.77
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.99
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.08
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.27
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.14
 p-value of test no 155                :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.46
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.11
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.68
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.04
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.98
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.74
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.20
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.91
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.34
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.51
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.07
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.92
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.18
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.61
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.80
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.48
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.30
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.24
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.79
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.55
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.99
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.28
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.46
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.18
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.91
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.17
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.34
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.54
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.86
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.76
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11455.32
 p-value of test no 229                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.20
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.87
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999945416
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.00
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999920945
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:35.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87228433.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56846
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.59
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.31
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.60
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.72
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.93
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.63
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.36
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.13
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.37
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.47
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.31
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.23
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.49
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.17
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908824
   j =  2                              :            45576
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908284
   j =  2                              :            45852
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.60
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.83
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.75
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.18
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.60
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.80
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 131                :    0.9915
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.45
 p-value of test no 133                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.70
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17569.18
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.85
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.18
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.78
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.04
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.50
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.50
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.07
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.79
 p-value of test no 154                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.90
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.57
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.67
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.55
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.99
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.63
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.60
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.76
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.26
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.33
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.45
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.14
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.55
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.03
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.12
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.87
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.51
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.48
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.96
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.04
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.02
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.12
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.73
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.95
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.36
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.76
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.40
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.76
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.94
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.04
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.21
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.10
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.74
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.35
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000019990
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.72
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999984122
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 238                :    0.03
 
 Sample variance                       :    2.19
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:12.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88277009.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56847
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997245
   j =  2                              :             1376
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    4.73
 p-value of test no 45                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.95
 p-value of test no 46                 :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.95
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.00
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.86
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.08
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.30
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.61
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.96
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.25
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
 p-value of test no 59                 :    0.9977
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.03
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.59
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.85
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.78
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908726
   j =  2                              :            45631
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908632
   j =  2                              :            45681
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 104                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 105                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.94
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.43
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.55
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.18
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.74
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.06
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.23
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.70
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.88
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.78
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.74
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.07
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.12
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.75
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.95
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.24
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.05
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.88
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.39
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.64
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.67
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.67
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.24
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.53
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.09
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.55
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.01
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.39
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.14
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.30
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.91
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.37
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.89
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.13
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.56
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.91
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.45
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.56
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :-7.02e-17
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.50
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.05
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.22
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9773.03
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.04
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.60
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.53
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.06
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.27
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11556.72
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.29
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.69
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999976781
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.55
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999921050
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.093
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:39.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89423889.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56848
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7518
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.70
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.63
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.23
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.16
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.75
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.81
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.57
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  162.35
 p-value of test no 67                 :  5.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.28
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908554
   j =  2                              :            45720
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46132
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907740
   j =  2                              :            46124
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.25
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.88
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.72
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.35
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.41
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.32
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.87
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.57
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-4
 p-value of test no 138                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  175.50
 p-value of test no 141                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.28
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.90
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.42
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.59
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.68
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.86
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.61
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.01
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.18
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.16
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.27
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.33
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.47
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.68
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.85
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.97
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.59
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.10
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.12
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.86
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.49
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.90
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.37
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.83
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.81
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.62
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.63
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.79
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.48
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.43
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.66
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.94
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.48
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9873.17
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.85
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.89
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.99
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.93
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.08
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.67
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.81
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.01
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000009316
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.57
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000002359
 
 Normal statistic for number of bits   :   0.019
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:57.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90275857.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56849
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 5                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.19
 p-value of test no 28                 :  7.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.36
 p-value of test no 41                 :  6.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.12
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.35
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.61
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.51
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.26
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.80
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.48
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.38
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.71
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.53
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.83
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.83
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.99
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.81
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.11
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908316
   j =  2                              :            45839
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908166
   j =  2                              :            45914
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.30
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.94
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.89
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.07
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.84
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.25
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.38
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.15
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.73
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.45
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.05
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.47
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.37
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.67
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.88
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.79
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.53
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.98
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.22
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.17
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.59
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.79
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.38
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.03
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.78
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.28
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.09
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.83
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.78
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.08
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.97
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.74
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.42
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.19
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.38
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.86
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.88
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.26
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.74
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.93
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.54
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.68
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.30
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.06
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.43
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.28
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.84
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.42
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.51
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.49
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.25
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.20
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.10
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000010840
 
 Normal statistic for number of bits   :   0.086
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.55
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999939182
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.36e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:02.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91258897.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56850
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 11                 :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.49
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.10
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.04
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.84
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.11
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.51
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.68
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.31
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.93
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.77
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.48
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.83
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.20
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907785
   j =  2                              :            46103
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46145
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907712
   j =  2                              :            46141
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
 p-value of test no 77                 :    0.9945
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.07
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.86
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.55
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.56
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.88
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.09
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.32
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.92
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.23
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.59
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.83
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.23
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.80
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.96
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.15
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.15
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.72
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.45
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.38
 p-value of test no 156                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.88
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.74
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.52
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.16
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.97
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.57
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.54
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.63
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.89
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.24
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5179.18
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.22
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.94
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.93
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.95
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.28
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.33
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.75
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.14
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 3.62e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.40
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.29
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.28
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.09
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.78
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.34
 p-value of test no 218                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.20
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.16
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3948.87
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4269.90
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.66
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.56
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.88
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999944582
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.26
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999882626
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:12.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9990 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  94  HammingCorr, L = 1200           0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92241937.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56851
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 14                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7524
 p-value of test no 21                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.29
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.84
 p-value of test no 48                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.91
 p-value of test no 49                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.48
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.10
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.98
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.35
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6872.52
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.45
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.67
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.40
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.11
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.29
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908673
   j =  2                              :            45659
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.02
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.53
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.50
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.72
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.29
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.67
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.90
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.41
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.72
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.28
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.94
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.63
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.77
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.03
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.46
 p-value of test no 155                :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.94
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.52
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.27
 p-value of test no 158                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.68
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.05
 p-value of test no 160                :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.21
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.17
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.18
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.52
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.64
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.64
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.95
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.20
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.82
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.22
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.00
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.85
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.64
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.70
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.18
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.00
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.58
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.47
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.14
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.88
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.01
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.06
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.40
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.31
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.22
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.84
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.89
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999998963
 
 Normal statistic for number of bits   : -8.20e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.18
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999826478
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:57.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93257745.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56852
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.39
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    3.32
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.97
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.23
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.68
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.87
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.42
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.38
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.12
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.52
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.09
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7189.75
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.27
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.52
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.59
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.43
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907939
   j =  2                              :            46026
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908236
   j =  2                              :            45873
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.90
 p-value of test no 117                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.36
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.82
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.48
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.49
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.95
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.83
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.78
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.74
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.82
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.17
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.32
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.50
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.74
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.31
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.35
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.98
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.10
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.54
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.05
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.78
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.61
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.47
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.41
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.64
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.30
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.35
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.20
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.43
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.22
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.58
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.09
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.38
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.33
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  266.03
 p-value of test no 170                :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.23
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.33
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.02
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.16
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.98
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 181                :    0.9913
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 183                :    0.9933
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.75
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.67
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.86
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.03
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 213                :  7.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.86
 p-value of test no 214                :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10411.97
 p-value of test no 215                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.10
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.25
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.32
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.17
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11360.61
 p-value of test no 229                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.80
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.13
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000033850
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.34
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999926051
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:30.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94339089.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56853
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.67
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.69
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.34
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.56
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.34
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.35
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.26
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.89
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.77
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.45
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.59
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.51
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.64
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908468
   j =  2                              :            45760
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907803
   j =  2                              :            46094
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.98
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.81
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.62
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.97
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.82
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.04
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.71
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.60
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 138                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.37
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.97
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.84
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.40
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.69
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.03
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.79
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.15
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.80
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.63
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.40
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.28
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.40
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.95
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.83
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.28
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.00
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.30
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.00
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.57
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.47
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.40
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.61
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.29
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.68
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.60
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.49
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.77
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.15
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.67
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.25
 p-value of test no 178                :  9.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 185                :  8.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 186                :    0.9942
 
 Anderson-Darling statistic = A2       :    5.92
 p-value of test no 187                :  1.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.41
 p-value of test no 188                :    0.9997    *****
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.76
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.93
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.10
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.81
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.05
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.12
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.38
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4318.41
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.49
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.22
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.21
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000028966
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.10
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999983930
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:56.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  83  LempelZiv, r = 15               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95387665.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56854
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.03
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.44
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.10
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.18
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.47
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.83
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.83
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.23
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.07
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.04
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.18
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.04
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.66
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907903
   j =  2                              :            46038
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-5
 p-value of test no 113                :    0.9915
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 115                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.86
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.25
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.83
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.94
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.91
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.84
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.96
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.58
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17325.64
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.15
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.73
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.08
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.18
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.92
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.72
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.14
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.32
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.44
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.10
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.73
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.56
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.34
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.52
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.09
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.97
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.93
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.33
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.46
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.80
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.11
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.29
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.07
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.78
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.23
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.38
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.54
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.25
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.60
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.75
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.41
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.87
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.84
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.94
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.56
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.18
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.81
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.90
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.58
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000147844
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.10
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999998378
 
 Normal statistic for number of bits   :  -0.013
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.60e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:23.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96403473.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56855
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 9                  :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.52
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    3.99
 p-value of test no 33                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.54
 p-value of test no 46                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.56
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.89
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.18
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.30
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.07
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.89
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.22
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.29
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.00
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.00
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.93
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.82
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.61
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907927
   j =  2                              :            46035
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908557
   j =  2                              :            45717
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.90e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.71
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.00
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.65
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.73
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.12
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.51
 p-value of test no 134                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.12
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.42
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.26
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.00
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.75
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.61
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.99
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.08
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.49
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.06
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.24
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.42
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.18
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.48
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.95
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.78
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.39
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.21
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.47
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.67
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.37
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.34
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.51
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.26
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.07
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.95
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.20
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.02
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.46
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.14
 p-value of test no 196                :  4.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.86
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.87
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.51
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.32
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.25
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.45
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.46
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.75
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.16
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.56
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.72
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999935375
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.81
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000055258
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:21.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           8.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97419281.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56856
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9911
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.22
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.21
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.49
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.66
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.44
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.78
 p-value of test no 52                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.73
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.10
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.66
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1519.49
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6867.12
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.17
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.17
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.24
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.60
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45544
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869544
   j =  1                              :        399908915
   j =  2                              :            45538
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908805
   j =  2                              :            45593
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 77                 :  8.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 78                 :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.35
 p-value of test no 115                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.62
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.71
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.91
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.73
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.38
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.77
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.19
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.49
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.87
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.30
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17078.98
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.40
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.57
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.65
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.72
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.00
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.83
 p-value of test no 154                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.63
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.99
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.41
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.81
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.58
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.59
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.03
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.97
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.01
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.08
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.90
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.60
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.43
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.22
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.18
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.26
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.27
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.78
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.82
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.14
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.86
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.37
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 205                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.60
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.15
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.20
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.73
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.90
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.31
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.19
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11548.26
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.58
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.65
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999981746
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.04
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999828416
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.017
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 250                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:59.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98402321.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56857
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997315
   j =  2                              :             1341
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    3.50
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.47
 p-value of test no 46                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.12
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.65
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.24
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.00
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.27
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.48
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.11
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.23
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.36
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.12
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.89
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.57
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.29
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5178.22
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908330
   j =  2                              :            45832
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45461
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869461
   j =  1                              :        399909080
   j =  2                              :            45457
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.57
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.28
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.35
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.48
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.42
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.22
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.13
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-3
 p-value of test no 131                :    0.9986
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.28
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.66
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17692.35
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.88
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.07
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.30
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.26
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.81
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.62
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.77
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.86
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.87
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.40
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.98
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.62
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.99
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.30
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.15
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.16
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.26
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.73
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.02
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.94
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.52
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.07
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.93
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.54
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.30
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.11
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.10
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.89
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.55
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.83
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.51
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.87
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.23
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.92
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.46
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.42
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.32
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.29
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999819134
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.63
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999826913
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:56.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99418129.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56858
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    3.96
 p-value of test no 27                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.60
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.08
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.13
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.45
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.17
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.85
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.10
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.51
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.04
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  375.85
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.76
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7080.81
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.07
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.14
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.20
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.69
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.29
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908072
   j =  2                              :            45961
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46225
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870225
   j =  1                              :        399907555
   j =  2                              :            46215
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.07
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.85
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.24
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.95
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.54
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.44
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.75
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.26
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.18
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17263.24
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.36
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.71
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.43
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.81
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.11
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.39
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.39
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.81
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.28
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.00
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.59
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.18
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.56
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.58
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.17
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.98
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.21
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.78
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.26
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5219.33
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.99
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.38
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.66
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.33
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.89
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.70
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.48
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.62
 p-value of test no 196                :    0.9905
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.23
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.47
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.64
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9761.16
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.52
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.46
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.04
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3933.19
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.26
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.79
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   92.10
 p-value of test no 231                :  9.5e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999992558
 
 Normal statistic for number of bits   :  -0.059
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.58
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999989078
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:16.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  101  Run of bits, r = 0              9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100466705.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56859
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7669
 p-value of test no 21                 :  2.4e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.24
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.38
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.40
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.93
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.98
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.08
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.85
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.08
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.92
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.50
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.36
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.35
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.05
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908164
   j =  2                              :            45909
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907837
   j =  2                              :            46077
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.42
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.13
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.79
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.34
 p-value of test no 122                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.97
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.58
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.80
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.35
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.27
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17766.19
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.83
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.61
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.32
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.93
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.10
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.49
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.76
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.95
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.00
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.66
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.34
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.51
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.69
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.56
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.78
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.73
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.20
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.74
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.55
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.19
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.98
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.46
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.15
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.28
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.37
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.68
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.05
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.44
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.56
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.76
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4700.35
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.29
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.03
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.38
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.57
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.80
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.10
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999939911
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.65
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999888263
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    2.48
 p-value of test no 244                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:36.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        2.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101482513.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56860
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7570
 p-value of test no 21                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.36
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.26
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.75
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.01
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.15
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.48
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.62
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.80
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.38
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.43
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.31
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.68
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908397
   j =  2                              :            45794
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45498
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869498
   j =  1                              :        399909007
   j =  2                              :            45492
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.34
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.69
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.75
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.48
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.43
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.40
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.47
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.77
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.97
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.33
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17431.94
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.12
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.04
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.30
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.67
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.45
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.69
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.42
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.02
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.33
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.60
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.38
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.99
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.98
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.15
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.10
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.39
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.11
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.31
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.76
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.25
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.34
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.37
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.16
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.84
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.95
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.42
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.17
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.18
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.45
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.29
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.67
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.43
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.69
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.76
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.86
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.95
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.11
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3925.25
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.25
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12160.58
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.18
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000086833
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.41
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999898982
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:08.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 81985538.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56861
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 9                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 12                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.50
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.18
 p-value of test no 34                 :  2.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    3.71
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.01
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.64
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.50
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.41
 p-value of test no 51                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.45
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.98
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.45
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.08
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7202.43
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.13
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.16
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.74
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4894.05
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907997
   j =  2                              :            45997
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908168
   j =  2                              :            45910
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.49
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.21
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.14
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.54
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.08
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.74
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.63
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.05
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17182.86
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.73
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.16
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.81
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.40
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.30
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.82
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.59
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.14
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.10
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.75
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.52
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.14
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.30
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.15
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.31
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.24
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.95
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.35
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.99
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.32
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.86
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.06
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.45
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.91
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.77
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.97
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.95
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.86
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.71
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.96
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.33
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.81
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.65
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.35
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.09
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.26
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.15
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.28
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.48
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.71
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999880877
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.09
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999912017
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:16.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83066882.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56862
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 8                  :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4200
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7535
 p-value of test no 19                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    3.42
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.49
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.50
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.14
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.63
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.82
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.29
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.82
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.17
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.02
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.59
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.90
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.20
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.05
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907941
   j =  2                              :            46019
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908208
   j =  2                              :            45893
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 105                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.13
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.79
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.79
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.40
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.06
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.96
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.24
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.95
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.72
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.65
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.89
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.66
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.74
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.42
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.52
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.90
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.32
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.01
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.63
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.92
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.71
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.03
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.88
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.75
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.96
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.36
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.35
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.00
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.72
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.49
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.73
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.70
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.47
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.85
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.78
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.02
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.52
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.62
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.62
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.34
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 192                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.53
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.81
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.73
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.35
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.24
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.89
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.25
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.50
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.01
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.97
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.42
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.38
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999981797
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.82
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999922478
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:12.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84049922.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56863
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    3.36
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.44
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.80
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.04
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.42
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.86
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.58
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.26
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.01
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.28
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.40
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.80
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.39
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.55
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.61
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46129
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870129
   j =  1                              :        399907743
   j =  2                              :            46127
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 99                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.15
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.23
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.38
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.96
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.24
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.54
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.92
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.93
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.06
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.57
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.86
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.25
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.53
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.43
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.75
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.09
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.76
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.67
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.15
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.75
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.09
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.04
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.47
 p-value of test no 161                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.78
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.97
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.18
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.30
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.82
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.30
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.57
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.32
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.52
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.69
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.32
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.16
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.04
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.17
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.48
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.11
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.28
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.31
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.38
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10348.66
 p-value of test no 211                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.87
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.04
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.12
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.15
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.37
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.47
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12159.19
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.04
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999860216
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.09
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000031252
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 236                :    0.9905
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:21.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85590018.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56864
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997295
   j =  2                              :             1351
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1516
 p-value of test no 12                 :  2.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334636
   j =  1                              :        599996968
   j =  2                              :             1516
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7573
 p-value of test no 15                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7590
 p-value of test no 20                 :  8.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9918
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.95
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.68
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.27
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.62
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.39
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.55
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.88
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.12
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.58
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.16
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.38
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.06
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908607
   j =  2                              :            45695
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908828
   j =  2                              :            45583
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.65
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.65
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.34
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.30
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.75
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.33
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.90
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.70
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 130                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.46
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.91
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17740.96
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.47
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.01
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.39
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.81
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.03
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.38
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.77
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.02
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.32
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.44
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.68
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.82
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.20
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.32
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.44
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.17
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.63
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.87
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.93
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.23
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.38
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.64
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.45
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.86
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.62
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.73
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.21
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.40
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.31
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.91
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.77
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.86
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.99
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.34
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.52
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.38
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.86
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.24
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.89
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.19
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.60
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.13
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999881225
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.71
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999988091
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    2.20
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:31.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.8e-5
  20  BirthdaySpacings, t = 16        8.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86507522.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56865
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.28
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.44
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.00
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.86
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.35
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.95
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.30
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.19
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.56
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.64
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.45
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5203.39
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907870
   j =  2                              :            46059
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45397
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869397
   j =  1                              :        399909208
   j =  2                              :            45393
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 101                :    0.9907
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 116                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.51
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.27
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.09
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.98
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.47
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.23
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.46
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.87
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.12
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.28
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.06
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.60
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.23
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.15
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.68
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.98
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.11
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.37
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.70
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.33
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.32
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.02
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.03
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.74
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.36
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.43
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.25
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.61
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.96
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.76
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.10
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.98
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.51
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.93
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.37
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.13
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.94
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.02
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.27
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.34
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.12
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.43
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.87
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.99
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.76
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9758.98
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.43
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.49
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.10
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.33
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.50
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.15
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.69
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999950801
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.13
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999905159
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:41.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87392258.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56866
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.73
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.22
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.22
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.88
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.70
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.53
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.48
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.63
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.23
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.08
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   21.77
 p-value of test no 66                 :  5.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.70
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.05
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45452
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869452
   j =  1                              :        399909100
   j =  2                              :            45444
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45505
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869505
   j =  1                              :        399908995
   j =  2                              :            45495
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.91
 p-value of test no 119                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.72
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.83
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.84
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.42
 p-value of test no 124                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.20
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.20
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.92
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.54
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.82
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.73
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.85
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.64
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.82
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.50
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.14
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.01
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.33
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.63
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.09
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.07
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.11
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.60
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.30
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.86
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.11
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.05
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.70
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.43
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.01
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.10
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.25
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.55
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.62
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.54
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.86
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.63
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.54
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 181                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 186                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 187                :  7.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.61
 p-value of test no 188                :  4.5e-3
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.21
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.42
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.39
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.07
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.23
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.71
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4727.51
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.08
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.96
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.22
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.97
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.64
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.79
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999857714
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.42
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000044980
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-3
 p-value of test no 251                :    0.9967
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:23.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              5.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88244226.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56867
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.53
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.04
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.78
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.65
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.07
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.83
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.23
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.24
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.76
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.15
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.20
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.02
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4820.22
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908243
   j =  2                              :            45871
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46286
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870286
   j =  1                              :        399907430
   j =  2                              :            46282
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.37
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.22
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.62
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.82
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.97
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.57
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.66
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.99
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.77
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.07
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.45
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.04
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.25
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.05
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.40
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.84
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.67
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.11
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.61
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.08
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.64
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.25
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.57
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.45
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.83
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.34
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.95
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.01
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.74
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.48
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.69
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.20
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.42
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.14
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.34
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.05
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.15
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.22
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.54
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.07
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.95
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.81
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.44
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.28
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.01
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.63
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.81
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.11
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.27
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.89
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.66
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.93
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999936053
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.42
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000078820
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:52.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89456642.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56868
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.62
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.77
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.82
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.69
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.67
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.87
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.86
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.90
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.76
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.11
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.25
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.17
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.36
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.63
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.11
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908205
   j =  2                              :            45893
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907744
   j =  2                              :            46122
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.76
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.31
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.85
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.15
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.12
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.80
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.26
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.51
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.19
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.67
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17769.29
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.78
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.13
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.53
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.88
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.57
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.88
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.83
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.64
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.80
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.68
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.64
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.59
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.04
 p-value of test no 163                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.70
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.68
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.92
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.04
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.42
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.43
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.41
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.54
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.06
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.88
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.89
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.68
 p-value of test no 175                :    0.9946
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.83
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 185                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.19
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
 p-value of test no 200                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  257.66
 p-value of test no 203                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.22
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.20
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.05
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5107.68
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.73
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.78
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.31
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.11
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.08
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.76
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999894638
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.71
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999953384
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:34.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90374146.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56869
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 6                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.66
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.02
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.45
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.02
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.84
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.97
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.99
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.70
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.23
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
 p-value of test no 58                 :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.50
 p-value of test no 61                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.07
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.47
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.40
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45981
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908042
   j =  2                              :            45973
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908175
   j =  2                              :            45908
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 101                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.36
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.52
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   74.14
 p-value of test no 123                :  2.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.44
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.70
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.61
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.21
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.68
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17223.17
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.38
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.85
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.37
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.11
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.35
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.87
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.99
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.95
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.02
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.22
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.81
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.74
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.58
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.39
 p-value of test no 160                :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.10
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.49
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.44
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.19
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  121.28
 p-value of test no 165                :  4.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.13
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.69
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.28
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.14
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.73
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.23
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.91
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.88
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.80
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.55
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.85
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.18
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.55
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.11
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.63
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.85
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.73
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.25
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.30
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.55
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.66
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.11
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000024607
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.17
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999936479
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:51.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           2.8e-4
  77  RandomWalk1 C (L=1000, r=20)    4.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91226114.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56870
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    3.44
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.32
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.16
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.61
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.80
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.67
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.80
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.71
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.12
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.15
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.20
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.51
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 62                 :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.46
 p-value of test no 65                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.27
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4841.35
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908711
   j =  2                              :            45643
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907805
   j =  2                              :            46096
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.16
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.70
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.18
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.66
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.39
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.78
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.15
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 126                :  3.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 127                :    0.9939
 
 Anderson-Darling statistic = A2       :    5.92
 p-value of test no 128                :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   16.33
 p-value of test no 129                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.38
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.85
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.54
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.17
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.26
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.55
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.59
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.70
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.96
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.83
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.77
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.71
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.74
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.79
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.74
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.29
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.04
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.38
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.61
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.14
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.56
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.51
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.12
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.30
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.85
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.19
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.20
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.54
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.07
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.29
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.82
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.91
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.08
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.86
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.06
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.89
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.28
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.24
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.54
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.43
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.07
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.14
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.79
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11434.03
 p-value of test no 230                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.55
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000117517
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.49
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000142759
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    2.04
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:32.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  66  MatrixRank, L=30, r=0           0.9997 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92536834.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56871
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.73
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.02
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.51
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.11
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.09
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.64
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.09
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.78
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6859.87
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.36
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.17
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.58
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5117.84
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908445
   j =  2                              :            45776
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908292
   j =  2                              :            45848
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
 p-value of test no 90                 :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.59
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.43
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.30
 p-value of test no 122                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.09
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.42
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.30
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.20
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.25
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.26
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.84
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.61
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.29
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.03
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.73
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   41.55
 p-value of test no 155                :  7.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.09
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.39
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.88
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.21
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.34
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.86
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.98
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.75
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.40
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.34
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.06
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.14
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.19
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.65
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.33
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.84
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.57
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.28
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.42
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.29
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.96
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.86
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.11
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.07
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.43
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.41
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.76
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.47
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.93
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.26
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.53
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.60
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000079507
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.14
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999964832
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    2.32
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:06.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 C (L=50, r=25)      7.8e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93421570.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56872
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.98
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.79
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.54
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.70
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.73
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.27
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.09
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.58
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6935.44
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.82
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.74
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.68
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.03
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908455
   j =  2                              :            45771
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908610
   j =  2                              :            45692
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 90                 :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 94                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 95                 :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  2.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.52
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.03
 p-value of test no 120                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.80
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.37
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.35
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.89
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.30
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.49
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.17
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.55
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.38
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.43
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.45
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.66
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.68
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.75
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.03
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.31
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.91
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.85
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.90
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.14
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.12
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.43
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.16
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.55
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.21
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.55
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.07
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  257.64
 p-value of test no 170                :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.32
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.18
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.83
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.76
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.99
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.34
 p-value of test no 176                :    0.9987
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.79
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   29.32
 p-value of test no 198                :  2.8e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.04
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.32
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.10
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.32
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.56
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.39
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4351.45
 p-value of test no 227                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.16
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.82
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.28
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.53
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000096811
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.68
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000025789
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:14.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  87  LongestHeadRun, r = 27          2.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94404610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56873
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997323
   j =  2                              :             1337
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    3.82
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.30
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.06
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.88
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.25
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.70
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.91
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.16
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.08
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.34
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.82
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.65
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908320
   j =  2                              :            45837
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907570
   j =  2                              :            46212
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 106                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.84
 p-value of test no 119                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.35
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.02
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.89
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.12
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.10
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.60
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.23
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17343.77
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.53
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.93
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.47
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.84
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.72
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.01
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.48
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.52
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.32
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.65
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.38
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.10
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.27
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.04
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.28
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.39
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.89
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.60
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.08
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4781.35
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.75
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.51
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.66
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.38
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.60
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.09
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.05
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    2.31
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.27
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.38
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.78
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.82
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.54
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.56
 p-value of test no 218                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.75
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.25
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.37
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.98
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11598.37
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11598.70
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.53
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000032776
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.25
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999935810
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.87
 p-value of test no 249                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 251                :    0.9926
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:47.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95289346.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56874
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 45                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.37
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.90
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.17
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.54
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.82
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.46
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.97
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.76
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.81
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7234.15
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.23
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.59
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.52
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.07
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908016
   j =  2                              :            45986
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908089
   j =  2                              :            45954
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.48
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.13
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.38
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.95
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.30
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.39
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.38
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.06
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.09
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.81
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.10
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.19
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.48
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.92
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.47
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.56
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.63
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.48
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.54
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.78
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.37
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.55
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.22
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.11
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.22
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.88
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.66
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.29
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.57
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.21
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.45
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.04
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.54
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.28
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.23
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.87
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.91
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.31
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.91
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.90
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.36
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.60
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.50
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.99
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.32
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.08
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.72
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4409.60
 p-value of test no 227                :  7.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.22
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.55
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.84
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.14
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999985919
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.17
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999998348
 
 Normal statistic for number of bits   :  -0.013
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    2.09
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:01.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  97  HammingIndep, L=300, r=0        7.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96337922.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56875
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.22
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.76
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.33
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.45
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.88
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  371.65
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.27
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.97
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.00
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.79
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.50
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4877.74
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907754
   j =  2                              :            46111
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908371
   j =  2                              :            45813
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 105                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.72
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.23
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.04
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.95
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.49
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.85
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.90
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.14
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.29
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.64
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.28
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.51
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.91
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.19
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.71
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.67
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.68
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.02
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.33
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.20
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.79
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.95
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.35
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.53
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.34
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.79
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.34
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.78
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.33
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.60
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.95
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.65
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.74
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.55
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.34
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.93
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.51
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.56
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.16
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.23
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.81
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.35
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.87
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.95
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.45
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.07
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.21
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.72
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.74
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.16
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.33
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.67
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.29
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999967913
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.60
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999982079
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:52.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97320962.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56876
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 9                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5581
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.06
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.93
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.18
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.60
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.68
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.08
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.65
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.85
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.22
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.54
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.68
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.21
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.01
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.20
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908162
   j =  2                              :            45916
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908000
   j =  2                              :            45994
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.95
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.86
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.06
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.72
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.25
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.04
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 127                :    0.9952
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.10
 p-value of test no 129                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.92
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.13
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.01
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17164.84
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.91
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.66
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.61
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.51
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.65
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.45
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.25
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.80
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.13
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.18
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.66
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.72
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.36
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.41
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.49
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.78
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.69
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.61
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.67
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.36
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.45
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.54
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.48
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.60
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.90
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.38
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.73
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.16
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.79
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.90
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.61
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9781.92
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 220                :    0.9924
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4660.88
 p-value of test no 222                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 223                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.43
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.19
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.58
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.11
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.64
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.40
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000028378
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.14
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999913040
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 238                :  9.2e-3
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.020
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:13.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98336770.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56877
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    3.39
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.95
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.88
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.60
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.24
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.34
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.30
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.52
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.43
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7157.88
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.23
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.95
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.64
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.08
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907857
   j =  2                              :            46067
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908386
   j =  2                              :            45801
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 74                 :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.20
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.84
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.23
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.29
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.09
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.36
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.54
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.92
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.30
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.89
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.07
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.17
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.08
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.64
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.48
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.68
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.88
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.78
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.06
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.70
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.93
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.58
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.43
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.11
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.95
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.21
 p-value of test no 163                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.64
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.47
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.33
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.17
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.57
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.27
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.90
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.09
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.54
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.54
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.85
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.25
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.44
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.71
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.98
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.88
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.75
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.81
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.52
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.71
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.03
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3963.67
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.40
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.80
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.38
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000107440
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.57
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000090916
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9965
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.026
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:48.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99287042.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56878
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.98
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.13
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.59
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.61
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.86
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.20
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.66
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7223.58
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.98
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.71
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.67
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5117.15
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908415
   j =  2                              :            45791
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908520
   j =  2                              :            45734
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.91
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.20
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.54
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.42
 p-value of test no 122                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.08
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.62
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.45
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.28
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.71
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17263.41
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.72
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.35
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.44
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.69
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.67
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.17
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.41
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.60
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.71
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.24
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.04
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.54
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.59
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.09
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.79
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.17
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.78
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.92
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.39
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.14
 p-value of test no 171                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.10
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.45
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.37
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.84
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.85
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.30
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.11
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 201                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.50
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.59
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.55
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.77
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.01
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.16
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.63
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.61
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.68
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.23
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.47
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000007588
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.52
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999832304
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:17.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100368386.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56879
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.10
 p-value of test no 35                 :  8.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    6.29
 p-value of test no 38                 :  7.3e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.13
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.83
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.66
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.51
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.83
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.64
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.87
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.77
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.21
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.47
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.47
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.81
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908447
   j =  2                              :            45769
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908293
   j =  2                              :            45846
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.30
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.47
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.04
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.56
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.91
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.55
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.67
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.57
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.78
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.64
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17270.30
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.36
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.38
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.96
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.28
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.29
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.59
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.29
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.80
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.97
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.62
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.15
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.56
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.37
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.21
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.76
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.14
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.43
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.59
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.67
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4776.60
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.64
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.18
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.39
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.15
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.95
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.13
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.94
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.96
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.53
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.73
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.31
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.77
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.93
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.31
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 223                :  3.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
 p-value of test no 224                :    0.9978
 
 Anderson-Darling statistic = A2       :    5.52
 p-value of test no 225                :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4588.94
 p-value of test no 226                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3915.01
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.50
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.59
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.25
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.07
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999862736
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.94
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999932882
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9943
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:25.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          7.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  96  HammingIndep, L=30, r=27        0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101351426.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56880
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.01
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.11
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.98
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.12
 p-value of test no 53                 :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.67
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.06
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.49
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.43
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.07
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.93
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.61
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.38
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.36
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45584
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908838
   j =  2                              :            45572
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907708
   j =  2                              :            46143
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-5
 p-value of test no 112                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.41
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.85
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.78
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.28
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.29
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 131                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.34
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.56
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17686.14
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.18
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.20
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.85
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.40
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.18
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.04
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.16
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.87
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.35
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.28
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.86
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.75
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.49
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.15
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.75
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.16
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.45
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.45
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.13
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.42
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.15
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.98
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.81
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.96
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.26
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.33
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.17
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.39
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.68
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 190                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.45
 p-value of test no 196                :  8.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.37
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.32
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.50
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.01
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.87
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.50
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.56
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.39
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.48
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.26
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.71
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.50
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000098188
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.22
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999965747
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:19.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82018307.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56881
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.57
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.52
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.62
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.62
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.47
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.39
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.72
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.38
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.60
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7232.00
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9970
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.22
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 62                 :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
 p-value of test no 63                 :    0.9981
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 64                 :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   31.51
 p-value of test no 65                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.07
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.80
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46093
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907816
   j =  2                              :            46089
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908176
   j =  2                              :            45909
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.55
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.61
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.03
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.53
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.23
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.74
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.78
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.99
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.27
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.85
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.00
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.15
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.86
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.70
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.53
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.02
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.35
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.15
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.86
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.95
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  189.16
 p-value of test no 159                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.08
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.25
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.25
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.89
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.39
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.94
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.84
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.39
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.81
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.99
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.83
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.19
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.19
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.10
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.61
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.09
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.45
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.27
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 200                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-3
 p-value of test no 201                :    0.9974
 
 Anderson-Darling statistic = A2       :    6.27
 p-value of test no 202                :  7.9e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  142.19
 p-value of test no 203                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.51
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.63
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.45
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.15
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 225                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.27
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3776.30
 p-value of test no 227                : 1 -  5.8e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.76
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.62
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.66
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.91
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000115573
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.03
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999933644
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.28
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.037
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:39.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     0.9991 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  88  PeriodsInStrings, r = 0         0.9993 
  97  HammingIndep, L=300, r=0       1 -  5.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83755011.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56882
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.53
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    3.36
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.06
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.68
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.22
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.86
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.35
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.61
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.21
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.52
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.79
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.03
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.13
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.49
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.42
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4752.37
 p-value of test no 68                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908567
   j =  2                              :            45715
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908256
   j =  2                              :            45872
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.49
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.53
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.24
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.11
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.15
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.92
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.65
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.04
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.80
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.29
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.74
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.18
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.98
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.56
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.07
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.78
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.91
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.20
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.57
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.75
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.38
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.16
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.00
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.25
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.38
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.72
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.08
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.50
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.89
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.22
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.74
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.88
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.08
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.93
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.79
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.62
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.62
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.75
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.80
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.49
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.40
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.40
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.23
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.40
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.71
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.22
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.21
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.27
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.43
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.43
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.80
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.17
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.72
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.26
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000012463
 
 Normal statistic for number of bits   :   0.099
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.93
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999924737
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 238                :    0.98
 
 Sample variance                       :    2.01
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:06.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84639747.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56883
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.27
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.95
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.81
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.88
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.06
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.47
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.79
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.22
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.47
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.46
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.54
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.99
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.46
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.96
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.09
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.18
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908118
   j =  2                              :            45932
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908211
   j =  2                              :            45893
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 91                 :    0.9922
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 97                 :  9.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    8.25
 p-value of test no 99                 :  9.4e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
 p-value of test no 104                :    0.9964
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.16
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.91
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.07
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.68
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.32
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.03
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.45
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.66
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.82
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.81
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.66
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.38
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.75
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.81
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.35
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.57
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.54
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.82
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.85
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.75
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.90
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.98
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.05
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.77
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.46
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.53
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.01
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.48
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.30
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.00
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.99
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.12
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.55
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.80
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.88
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.38
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.59
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.13
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.46
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.48
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.84
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.26
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.24
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.12
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.72
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.68
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.33
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.09
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.62
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.54
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.22
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.09
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999905951
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.20
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999990368
 
 Normal statistic for number of bits   :  -0.076
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    2.06
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    2.94
 p-value of test no 249                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 251                :    0.9958
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:05.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               9.4e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85524483.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56884
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 5                  :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 7                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.19
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.02
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.60
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.22
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.47
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.26
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.93
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.91
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7196.10
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.06
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.92
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.47
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.44
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.05
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907923
   j =  2                              :            46037
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46295
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870295
   j =  1                              :        399907411
   j =  2                              :            46293
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.83
 p-value of test no 118                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.31
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.37
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.88
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.66
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.20
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.31
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.28
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.89
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.84
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.43
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.43
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.12
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.72
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.01
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.25
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.92
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.87
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.60
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.91
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.55
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.37
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.74
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.42
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.49
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.38
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.92
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.58
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.11
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.26
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.71
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.87
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.24
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.33
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.17
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.19
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.00
 p-value of test no 174                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.79
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.40
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.77
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    2.03
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.88
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.96
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.31
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.49
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.35
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.50
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.89
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.69
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.60
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.79
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.54
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000010405
 
 Normal statistic for number of bits   :   0.082
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.50
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999985769
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:55.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            8.6e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86278147.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56885
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1224
 p-value of test no 12                 : 1 -  6.0e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334344
   j =  1                              :        599997552
   j =  2                              :             1224
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5570
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    3.88
 p-value of test no 27                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.07
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.54
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.28
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.91
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.33
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.33
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.11
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.16
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.19
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.21
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.62
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908400
   j =  2                              :            45794
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908683
   j =  2                              :            45657
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.28
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.96
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.22
 p-value of test no 122                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.00
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.83
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.85
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.25
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.85
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.51
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.29
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.98
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.70
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.78
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.74
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.17
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.57
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.38
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.78
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.77
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.76
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.11
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.91
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.51
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.52
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.95
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.20
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.30
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.00
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.97
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.17
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.96
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.11
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.76
 p-value of test no 172                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.17
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.32
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  271.56
 p-value of test no 175                :  5.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.69
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.65
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    2.09
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.54
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.01
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.17
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.89
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.28
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.18
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.79
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.69
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.38
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.38
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.31
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999960983
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.33
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000059569
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:43.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  6.0e-5
  79  RandomWalk1 C (L=10000, r=15)   5.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87293955.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56886
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1518
 p-value of test no 12                 :  2.3e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334638
   j =  1                              :        599996964
   j =  2                              :             1518
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     822
 p-value of test no 25                 :    0.9956
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    7.85
 p-value of test no 30                 :  1.4e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     668
 p-value of test no 31                 :  3.3e-3
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 35                 :    0.9974
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.91
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.25
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.06
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.60
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.09
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.39
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.11
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.00
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.21
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.34
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.72
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.39
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.39
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.17
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908324
   j =  2                              :            45832
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908242
   j =  2                              :            45876
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-4
 p-value of test no 112                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.88
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.14
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.63
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.39
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.39
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.17
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.22
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.24
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.68
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.65
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.20
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.39
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.70
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.65
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.79
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.28
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.01
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.51
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.75
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.32
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.20
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.87
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.10
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.85
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.63
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.13
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.27
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.24
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.94
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.86
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.95
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.06
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.45
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.11
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.84
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.91
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.49
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.00
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.00
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.75
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-4
 p-value of test no 190                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.57
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.64
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.70
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.28
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.95
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.78
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.80
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.61
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.53
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.58
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11497.99
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.91
 p-value of test no 231                :  2.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999861920
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.89
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999895652
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.13
 p-value of test no 244                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:09.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.3e-5
  23  ClosePairs mNP1, t = 5          1.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88375299.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56887
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.33
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.70
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.98
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.85
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.76
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.25
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.50
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.24
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.66
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.87
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.52
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.03
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.19
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907860
   j =  2                              :            46067
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908828
   j =  2                              :            45580
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.97
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.39
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.45
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.81
 p-value of test no 122                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.18
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.81
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.99
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.48
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.46
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.22
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.85
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.99
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.74
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.39
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.81
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.71
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.00
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.64
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.32
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.45
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.17
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.31
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.06
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.06
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.25
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.45
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.10
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.84
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.48
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.55
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.74
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.56
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.84
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.78
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.59
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.91
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.94
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.58
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.13
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 205                :    0.9950
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.76
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.64
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.52
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.68
 p-value of test no 218                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.00
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.09
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.63
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.88
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.98
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.38
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.28
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999847097
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.45
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999913037
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:42.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89554947.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56888
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 11                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 12                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.78
 p-value of test no 41                 :  4.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.49
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.31
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.82
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.33
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.93
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.93
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.19
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.98
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.46
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.56
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.91
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.07
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.06
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5275.89
 p-value of test no 68                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908053
   j =  2                              :            45966
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907848
   j =  2                              :            46073
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.93
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.07
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.64
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.14
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.35
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.02
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.38
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.94
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.47
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.19
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 138                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.92
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.92
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.04
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.26
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.56
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   67.24
 p-value of test no 152                :  8.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.83
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.56
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.20
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.22
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.06
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.82
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.56
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.04
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.60
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.03
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.28
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.04
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.45
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.52
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.31
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.83
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.08
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.33
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.46
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.94
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.60
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.90
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.07
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.91
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.16
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.22
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 213                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10251.61
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.29
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.31
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.24
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.86
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.39
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12107.95
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.14
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000054454
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.41
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000018286
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:29.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 M (L=50, r=25)      8.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90832899.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56889
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    3.73
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.04
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.80
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.16
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.04
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.21
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.58
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.34
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.62
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.73
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.50
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.86
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 62                 :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.39
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.10
 p-value of test no 66                 :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.93
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.56
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908639
   j =  2                              :            45676
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46379
 p-value of test no 71                 :  1.0e-2
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870379
   j =  1                              :        399907243
   j =  2                              :            46377
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.70
 p-value of test no 115                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.98
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.15
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.16
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.28
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.58
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.48
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.59
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.44
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.57
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.38
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.79
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.91
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.69
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.94
 p-value of test no 152                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.15
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.84
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.40
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.69
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.69
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.54
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.10
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.40
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.82
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.83
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.08
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.47
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.99
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.91
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.61
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.94
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.34
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.06
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.50
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.25
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.43
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.58
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.10
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.73
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.29
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.69
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.56
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.91
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.60
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.91
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.57
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.95
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.89
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.89
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999922877
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.83
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000048730
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:35.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91947011.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56890
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4160
 p-value of test no 14                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.72
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.04
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.12
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.07
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.54
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.86
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.85
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.23
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.29
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.45
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.24
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.14
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907987
   j =  2                              :            46002
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908456
   j =  2                              :            45766
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.15
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.87
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.88
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.46
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.61
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.23
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.28
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.59
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.26
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.50
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17296.08
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.54
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.90
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.43
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.34
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.55
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.90
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.39
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.90
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.17
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.61
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.38
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.90
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.29
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.75
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.35
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.86
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.01
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.92
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.57
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.02
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.87
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.24
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.48
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.16
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.58
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.85
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.37
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.88
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   33.48
 p-value of test no 176                :  8.1e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.13
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.31
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.82
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.69
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.98
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.66
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.03
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.29
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.01
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.11
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.05
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.91
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000098284
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.93
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000140809
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:36.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  80  LinearComp, r = 0               8.1e-4
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93061123.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56891
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    3.04
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     830
 p-value of test no 25                 :    0.9904
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.44
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.39
 p-value of test no 48                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.07
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.02
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.98
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.93
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.58
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.46
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.26
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.78
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.06
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.32
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908018
   j =  2                              :            45982
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907899
   j =  2                              :            46037
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.54
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.67
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.65
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.47
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.42
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.88
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 131                :    0.9907
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.88
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.74
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17731.94
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.58
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.91
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.84
 p-value of test no 149                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.35
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.19
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.22
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.69
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.37
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.84
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.84
 p-value of test no 159                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.40
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.66
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.17
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.25
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.92
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.82
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.43
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.57
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.86
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.32
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.15
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.18
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.11
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.43
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.20
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.91
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.94
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.67
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.86
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.09
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.13
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.49
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.36
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.80
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.33
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.50
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12240.86
 p-value of test no 230                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.24
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000148486
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.21
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000130468
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.11
 p-value of test no 239                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:33.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94076931.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56892
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4118
 p-value of test no 14                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   23.02
 p-value of test no 46                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.80
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.60
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.21
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.87
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.74
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.54
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.20
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.85
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.51
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.36
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.47
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.46
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.67
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.00
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.60
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908375
   j =  2                              :            45805
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908826
   j =  2                              :            45581
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 74                 :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  9.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 87                 :    0.9933
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9907
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.07
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.40
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.41
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.91
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.21
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.45
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.98
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 126                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.70
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.46
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.24
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.39
 p-value of test no 135                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 140                :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.21
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17041.45
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.19
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.30
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.15
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.21
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.73
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.40
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.69
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.74
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.82
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.57
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.53
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.35
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.44
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.90
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.13
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.80
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.21
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.08
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.47
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.12
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.38
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.79
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.30
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.66
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.58
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.58
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.23
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.31
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.33
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.31
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 181                :    0.9922
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 182                :  7.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.76
 p-value of test no 183                :    0.9971
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.56
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.02
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.08
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.39
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.80
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.57
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.30
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.21
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.23
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11531.62
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.43
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.64
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999895280
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.74
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000053431
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:58.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95092739.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56893
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.9916
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.86
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.78
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.59
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.81
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.32
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.73
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.01
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.96
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7156.53
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.70
 p-value of test no 59                 :  2.9e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.09
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.70
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.63
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.65
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.00
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907758
   j =  2                              :            46118
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908512
   j =  2                              :            45738
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.67
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.06
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.90
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.76
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.28
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.02
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.24
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.04
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.38
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17559.23
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.73
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.53
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.36
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.33
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.61
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.42
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.67
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.45
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.77
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.12
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.54
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.18
 p-value of test no 159                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.39
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.03
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.50
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.20
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.52
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.01
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.54
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.94
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.51
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.85
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.22
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.68
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.39
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.98
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.36
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.07
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.20
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.88
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.27
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.59
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.19
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.66
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.71
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.24
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.39
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.34
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.22
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.84
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000060280
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.53
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000042058
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:25.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96075779.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56894
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9937
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     115
 p-value of test no 43                 :    0.9983
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.81
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.53
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.03
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.94
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.38
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.22
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.28
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1339.69
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.36
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.79
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.39
 p-value of test no 65                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.36
 p-value of test no 66                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.39
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.44
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908266
   j =  2                              :            45864
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908662
   j =  2                              :            45666
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.71e-4
 p-value of test no 109                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.84
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.61
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.70
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.41
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.75
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.19
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.86
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.13
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.02
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.77
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.86
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17646.54
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.81
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.54
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.51
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.63
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.70
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.84
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.85
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.09
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.37
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.41
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.35
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.70
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.70
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.63
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.09
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.15
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.12
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.00
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.96
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.37
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.44
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.68
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.81
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.57
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.08
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.65
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.58
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.67
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.55
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.20
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.74
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.41
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.91
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.61
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.20
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12119.24
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.02
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.84
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000007636
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.29
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999899852
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:52.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97091587.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56895
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.62
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.73
 p-value of test no 50                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.62
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.49
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.22
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.78
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.16
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7213.05
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.37
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.61
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.36
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4739.22
 p-value of test no 68                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908159
   j =  2                              :            45913
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907943
   j =  2                              :            46021
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.78
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.83
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.15
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.43
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.13
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.21
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.53
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.74
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.50
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.24
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.55
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.56
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.27
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.04
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.88
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.87
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.22
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.89
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.82
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.40
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.26
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.22
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.24
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.95
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.01
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.28
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.11
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.22
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.79
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.99
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.46
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.85
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.63
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4775.89
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.04
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.08
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.75
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.91
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.50
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.92
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.82
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.21
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.14
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.58
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3868.18
 p-value of test no 227                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.29
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12015.94
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.41
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.18
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999888497
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.04
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999860285
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:39.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98107395.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56896
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5623
 p-value of test no 13                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.95
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.40
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.75
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.74
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.34
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.80
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.93
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.20
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.93
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.49
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.24
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.71
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907743
   j =  2                              :            46121
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908428
   j =  2                              :            45780
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.12
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.52
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.15
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.97
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.99
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.23
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.06
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.19
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.54
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.67
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.44
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.50
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.57
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.27
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.76
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.85
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.52
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.67
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.14
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.36
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.80
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.16
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.80
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.77
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.02
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.11
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.77
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.10
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.10
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.34
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.36
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.40
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.01
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.85
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.71
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.83
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.30
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.09
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.65
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.67
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.80
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.43
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.36
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.52
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.58
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.85
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.08
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.40
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12372.95
 p-value of test no 229                :  2.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.11
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.26
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000002194
 
 Normal statistic for number of bits   :   0.017
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.73
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999880607
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    2.08
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:12.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  99  HammingIndep, L=1200, r=0       2.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99155971.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56897
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5565
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9914
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.12
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.25
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.96
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.53
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.30
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.72
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  369.95
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.82
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.39
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.44
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.02
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.00
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45636
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908729
   j =  2                              :            45634
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908012
   j =  2                              :            45988
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.91
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.45
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.16
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.11
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.91
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.34
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.02
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.31
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.77
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.40
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17491.42
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.10
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.38
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.43
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.53
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.43
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.03
 p-value of test no 151                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.52
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.46
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.92
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.59
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.20
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.61
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.19
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.64
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.48
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.72
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.37
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.49
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.35
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.23
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.18
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.52
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.39
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.56
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.26
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.70
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.40
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.23
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.71
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.31
 p-value of test no 198                :    0.9954
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.76
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.44
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.45
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 214                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9663.73
 p-value of test no 215                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.19
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.87
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.64
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.03
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.46
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.83
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.08
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999920375
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.27
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000117031
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:30.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100171779.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56898
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    3.18
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.98
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.42
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.37
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.50
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.46
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.99
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.09
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.94
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.00
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.27
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.00
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.99
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.25
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908581
   j =  2                              :            45705
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-4
 p-value of test no 97                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  5.3e-3
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 99                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
 p-value of test no 104                :    0.9930
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.94
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.34
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.40
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.94
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.14
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.09
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.42
 p-value of test no 135                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.59
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.16
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.47
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.20
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.18
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.60
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.11
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.66
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.20
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.68
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.50
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.11
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.47
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.18
 p-value of test no 161                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.23
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.48
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.75
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.21
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.14
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.49
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.36
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.25
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.36
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.88
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.74
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.17
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.46
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.72
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.10
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9973
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.04
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.15
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.77
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.15
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9837.12
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.95
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.89
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.08
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.18
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.92
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.25
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.65
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.94
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999956870
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.66
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999883289
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:38.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101154819.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56899
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997257
   j =  2                              :             1370
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.92
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.10
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.19
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.39
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.13
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.39
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.82
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7042.29
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.64
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.17
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.59
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.34
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.61
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907941
   j =  2                              :            46025
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45451
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869451
   j =  1                              :        399909102
   j =  2                              :            45443
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-4
 p-value of test no 76                 :    0.9990
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-4
 p-value of test no 101                :    0.9990
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.82
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.60
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.11
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.23
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.53
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.58
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.89
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.91
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.89
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.12
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.93
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.90
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.40
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.78
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.20
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.88
 p-value of test no 152                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.03
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.82
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.67
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.46
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.54
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.44
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.00
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.06
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.97
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.30
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.40
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.87
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.98
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.75
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.18
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.24
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.34
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.60
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.25
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.49
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.44
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.92
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.21
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.56
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.09
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.36
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.50
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.27
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.96
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.45
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.39
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.61
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.37
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.96
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999996833
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.05
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999957368
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:32.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102105091.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56900
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.22
 p-value of test no 46                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.45
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.62
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.94
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.09
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.87
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.90
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.13
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.58
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.41
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.51
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.02
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.59
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.24
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.97
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908696
   j =  2                              :            45643
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907749
   j =  2                              :            46118
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-3
 p-value of test no 77                 :    0.9988
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.02
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.93
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.62
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.79
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.45
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.23
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.19
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.70
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.33
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.18
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.08
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.50
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.35
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.80
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.42
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.08
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.22
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.75
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.52
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.21
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.90
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.35
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.57
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.71
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.45
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.15
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.72
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.78
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.43
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.32
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.61
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.10
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.57
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.33
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.33
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.68
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.43
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.76
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.83
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.29
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.87
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.83
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.61
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.51
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.36
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.70
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.26
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.00
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.17
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.94
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.72
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.80
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000198121
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.93
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999941321
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    3.46
 p-value of test no 254                :  2.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:39.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82051076.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56901
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 11                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.32
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.13
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.65
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.07
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.11
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.17
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1547.82
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.16
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.05
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.13
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.78
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5182.99
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908060
   j =  2                              :            45967
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908604
   j =  2                              :            45692
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-3
 p-value of test no 86                 :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.05
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.51
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.16
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.05
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.27
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.02
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.51
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.18
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.59
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 140                :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   89.48
 p-value of test no 141                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.82
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.43
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.18
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.67
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.13
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.97
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.72
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.69
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.61
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.17
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.74
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.95
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.73
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.70
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.84
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.31
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.57
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.32
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.48
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.57
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.70
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.82
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.90
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.98
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.83
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.67
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.10
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.52
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.87
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.96
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.96
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.84
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.17
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.26
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.28
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.31
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.62
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.29
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.94
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.65
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.55
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11546.28
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11623.51
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.94
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000034873
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.22
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999807401
 
 Normal statistic for number of bits   :   -1.52
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:50.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83329028.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56902
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9935
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.51
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.18
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.21
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.04
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.64
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.23
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.89
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.72
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.79
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.06
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.66
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.21
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.23
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.16
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907975
   j =  2                              :            46002
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907869
   j =  2                              :            46064
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.44e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.33
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.72
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.52
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.12
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.76
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.17
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.52
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.35
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.02
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.04
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.67
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.59
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.04
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.47
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.14
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.00
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.97
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.14
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.40
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.49
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.13
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.91
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.34
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.27
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.19
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.81
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.47
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.26
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.94
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.40
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.57
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.96
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.68
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.41
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.06
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.89
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.15
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.17
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.80
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.38
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.02
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.11
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.08
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.22
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.77
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.73
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.49
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.29
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.46
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000060706
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.41
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999803030
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:03.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84541458.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56903
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 6                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 41                 :    0.9952
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.67
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.12
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.85
 p-value of test no 49                 :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.85
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.49
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.94
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.93
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.94
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.41
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.38
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.03
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.05
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.36
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.95
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.76
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45570
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869570
   j =  1                              :        399908862
   j =  2                              :            45566
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908660
   j =  2                              :            45661
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.79
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.66
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.30
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.99
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.89
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.93
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.45
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17639.63
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.76
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.02
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.97
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.93
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.26
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.46
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.24
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.07
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.25
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.47
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.20
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.40
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.35
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.37
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4756.81
 p-value of test no 168                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.61
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.79
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.56
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.24
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.34
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.36
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.95
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.47
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.21
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 180                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.07
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.73
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 199                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.27
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.04
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.57
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.92
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.75
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 223                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5096.60
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.65
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.81
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11514.11
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11528.01
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.42
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000067837
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.08
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000223768
 
 Normal statistic for number of bits   :    1.77
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    2.84
 p-value of test no 244                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:55.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85295122.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56904
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1248
 p-value of test no 11                 :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334368
   j =  1                              :        599997504
   j =  2                              :             1248
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.87
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.08
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.86
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.62
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.93
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.47
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.79
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.67
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.81
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.00
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.63
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5164.89
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907709
   j =  2                              :            46141
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908177
   j =  2                              :            45907
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 106                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.49
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.63
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.71
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.67
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.54
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.91
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.28
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.75
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.02
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.76
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17664.25
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.31
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.27
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.75
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.74
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.29
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.53
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.43
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.83
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.06
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.48
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.98
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.50
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.03
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.17
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.68
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.08
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.54
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.52
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.44
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.03
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.60
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.38
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.01
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.54
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.14
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.38
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.87
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.15
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.30
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.16
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.07
 p-value of test no 207                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.88
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.50
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.10
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.38
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.15
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.43
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.93
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.20
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.61
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000072898
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.68
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000100822
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.086
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:40.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86147090.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56905
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.24
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.62
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.58
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.55
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.95
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.98
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.67
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.48
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.12
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1308.79
 p-value of test no 56                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.61
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 60                 :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.59
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.03
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.98
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.85
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45486
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869486
   j =  1                              :        399909032
   j =  2                              :            45478
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908276
   j =  2                              :            45859
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 111                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.41
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.34
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.45
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.71
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.55
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.88
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.82
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.58
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.18
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.24
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.76
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.15
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.19
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.44
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.26
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.06
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.12
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.00
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.50
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.49
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.86
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.24
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.58
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.01
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.21
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.07
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.82
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.17
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.48
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.07
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.99
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.92
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.66
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.45
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.27
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.00
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.30
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.50
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.74
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.09
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.42
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.87
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.16
 p-value of test no 198                :  4.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.98
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.38
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.82
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.49
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 221                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4627.45
 p-value of test no 222                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.70
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.86
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.40
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11541.42
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.19
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.96
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000045274
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.27
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000012370
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 237                :    0.9944
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.045
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:03.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87162898.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56906
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 5                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    3.40
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.91
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.47
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.79
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.04
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.98
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.51
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.88
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.26
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.66
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.09
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.15
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.78
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.41
 p-value of test no 66                 :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.26
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.59
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908360
   j =  2                              :            45814
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907975
   j =  2                              :            46005
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 76                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
 p-value of test no 83                 :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.56e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.27
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.00
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.33
 p-value of test no 121                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.11
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.33
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.81
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.28
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.26
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.56
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.60
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.41
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.74
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.06
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.94
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.51
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.95
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.04
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.02
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.56
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.99
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.54
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.83
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.34
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.05
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.78
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.24
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.72
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.89
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.35
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.32
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.74
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.18
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.32
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.40
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.76
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.95
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.43
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.05
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.80
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.34
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.44
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.22
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.40
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.40
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.01
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.58
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.71
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.83
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.68
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.56
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.40
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.93
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.11
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999973139
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.21
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000085567
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    2.29
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:39.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88178706.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56907
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.61
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.25
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.15
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.55
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.44
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.69
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.90
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.04
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.74
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.01
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.61
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46176
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870176
   j =  1                              :        399907649
   j =  2                              :            46174
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908553
   j =  2                              :            45722
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-4
 p-value of test no 98                 :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.40
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.60
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.83
 p-value of test no 121                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.48
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.77
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.22
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.36
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.56
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.00
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17273.50
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.06
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.10
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.47
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.93
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.06
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.90
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.17
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.37
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.85
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.28
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.82
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.71
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.30
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.57
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.62
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.40
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.97
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.44
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5222.81
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.53
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.76
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.73
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.25
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.59
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.31
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.65
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.15
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.20
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.75
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.30
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.76
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.90
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.42
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.99
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.71
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.82
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12307.89
 p-value of test no 229                :  9.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.27
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.67
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999980921
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.31
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999935825
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 252                :    0.9972
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.089
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:34.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  99  HammingIndep, L=1200, r=0       9.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89128978.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56908
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1490
 p-value of test no 12                 :  4.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334610
   j =  1                              :        599997020
   j =  2                              :             1490
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    6.76
 p-value of test no 27                 :  4.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.79
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.56
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.56
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.57
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.54
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.32
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7186.18
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.50
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   97.70
 p-value of test no 65                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.95
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.89
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4866.54
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45565
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908874
   j =  2                              :            45557
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45600
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908801
   j =  2                              :            45598
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 3.31e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.68
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.92
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.44
 p-value of test no 122                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.37
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.35
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.40
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.50
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.096
 p-value of test no 134                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.94
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.06
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.18
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.09
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.05
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.52
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.94
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.23
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.05
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.22
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.55
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.44
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.44
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.55
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.09
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.68
 p-value of test no 161                :  1.0e-2
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.16
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.84
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.93
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.19
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.46
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.41
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.86
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.61
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.57
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.77
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.22
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.56
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.43
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.31
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.51
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.46
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.32
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.23
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.90
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5044.53
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.52
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.42
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3897.95
 p-value of test no 228                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.14
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.77
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.81
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000046090
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.08
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999966950
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.15
 p-value of test no 254                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:34.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           4.1e-4
  22  ClosePairs mNP2S, t = 3         4.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90112018.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56909
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 4                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9909
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.18
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.60
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.57
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.55
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.65
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.36
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.65
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.44
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.67
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.10
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.57
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.16
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.06
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46145
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907714
   j =  2                              :            46137
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908508
   j =  2                              :            45740
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 84                 :    0.9905
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 101                :    0.9938
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-5
 p-value of test no 113                :    0.9934
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.13
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.18
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.49
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.38
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.84
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.34
 p-value of test no 125                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.06
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.93
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.91
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.77
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.21
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.17
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.61
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.13
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.99
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.56
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.70
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.90
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.25
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.42
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.73
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.85
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.38
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.77
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.52
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.36
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.24
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.66
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.37
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.94
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.80
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.27
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.70
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.45
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.78
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.58
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.39
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.79
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.30
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.69
 p-value of test no 198                :  5.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.22
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.81
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.31
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.50
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.18
 p-value of test no 217                :  7.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.85
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.43
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.21
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.25
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.62
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.97
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.05
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999854096
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.38
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000147301
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 243                :    0.98
 
 Sample variance                       :    2.20
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:03.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  93  HammingCorr, L = 300            7.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91160594.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56910
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.48
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.22
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.32
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.63
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.38
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.19
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.35
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.05
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.14
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.26
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6728.51
 p-value of test no 57                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.68
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.53
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.98
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.40
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907717
   j =  2                              :            46134
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46368
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870368
   j =  1                              :        399907268
   j =  2                              :            46360
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.02e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.09
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.95
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.96
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.46
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.07
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.94
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.94
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.59
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.081
 p-value of test no 135                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.10
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.39
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.21
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.58
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.17
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.82
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.65
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.21
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.58
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.35
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.41
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.52
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.72
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.33
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.84
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.57
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.03
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.06
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.16
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.88
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.69
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.39
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.49
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.63
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5239.80
 p-value of test no 173                :  9.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.06
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.15
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.15
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.95
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.84
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.99
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-4
 p-value of test no 190                :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.26
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.36
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.47
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.97
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.49
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.70
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.15
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.41
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.73
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.11
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.96
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.52
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000055609
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.58
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000010801
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
 p-value of test no 241                :    0.9975
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.080
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:22.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92143634.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56911
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4476
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.25
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.77
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.28
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.16
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.83
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.26
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.30
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.23
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.65
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.90
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.18
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4806.93
 p-value of test no 68                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908297
   j =  2                              :            45844
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908521
   j =  2                              :            45735
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.21
 p-value of test no 118                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.15
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.20
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.40
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.24
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.30
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.81
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 127                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.97
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.87
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.86
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.13
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.97
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.08
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.70
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.47
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.60
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.75
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.50
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.56
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.35
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.42
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.45
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.91
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.23
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.29
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.49
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.58
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.12
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.61
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.44
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.97
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.31
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4801.83
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.45
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.26
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.85
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.64
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.52
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.23
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.41
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.78
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.91
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.15
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.32
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.17
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.80
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.16
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.32
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.10
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.78
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.00
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.94
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.85
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000004543
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.17
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999965678
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:59.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  58  AppearanceSpacings, r = 27      0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93126674.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56912
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.03
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.45
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.95
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.03
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.53
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.46
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.79
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.95
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.75
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.59
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.07
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.82
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.37
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.01
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.66
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908078
   j =  2                              :            45958
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908434
   j =  2                              :            45780
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.32
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.54
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.84
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.68
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.82
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.20
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.27
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.31
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.99
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.35
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.00
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.00
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.67
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.11
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.50
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.61
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.38
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.56
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.37
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.07
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.33
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.12
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.66
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.60
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.33
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.63
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.44
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.55
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.84
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.75
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.64
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.29
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.22
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.78
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.38
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.49
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.31
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.02
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.20
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.73
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.40
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.10
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9837.18
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.11
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.97
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.46
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.02
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.06
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11577.64
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.03
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.55
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999942662
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.23
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999837242
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:21.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94142482.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56913
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7107
 p-value of test no 20                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    5.46
 p-value of test no 38                 :  1.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.70
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.23
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.35
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.05
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.71
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.54
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.18
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.60
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.01
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.45
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.99
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.21
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.87
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.92
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908054
   j =  2                              :            45967
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908357
   j =  2                              :            45814
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.69
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.97
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.51
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.73
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.14
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.27
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.57
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.55
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.99
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.49
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17324.23
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.26
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.15
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.44
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.41
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.23
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.85
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.04
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.83
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.94
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.04
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.99
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.09
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.19
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.34
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.72
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.30
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.80
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.02
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.65
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.04
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.06
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.14
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.15
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.14
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.02
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.01
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.16
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.19
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.52
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.27
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.49
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.78
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10308.93
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.21
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.19
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.49
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.76
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.09
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.12
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11449.90
 p-value of test no 230                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.16
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999959027
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.01
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000024715
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 238                :    0.87
 
 Sample variance                       :    2.20
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:17.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95158290.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56914
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    3.97
 p-value of test no 27                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.77
 p-value of test no 48                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.55
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.77
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.78
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.19
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.80
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.38
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.50
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.83
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.86
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.13
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.42
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.24
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.95
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908659
   j =  2                              :            45669
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908538
   j =  2                              :            45728
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.66
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.96
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.96
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.12
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.29
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.66
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.29
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.47
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.08
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.14
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.23
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.76
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.79
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.77
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.12
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.29
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.12
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.68
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.13
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.20
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.11
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.80
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.82
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.61
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.18
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.81
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.95
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.21
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.55
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.69
 p-value of test no 166                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.57
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.21
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.23
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.94
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.27
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.80
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.43
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.77
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.97
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.64
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.31
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.50
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.92
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.80
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.01
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.05
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.37
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.65
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11559.51
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.41
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000066202
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.71
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000035137
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:44.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96174098.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56915
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.19
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.78
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.43
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.13
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.70
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.47
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.89
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.04
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.75
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.92
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.67
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.86
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.18
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.59
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46196
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907614
   j =  2                              :            46184
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
 p-value of test no 80                 :    0.9938
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9962
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  6.6e-3
 
 Anderson-Darling statistic = A2       :    5.03
 p-value of test no 95                 :  2.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  2.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.36
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.24
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.61
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.72
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.23
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.78
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.05
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.77
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.03
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.38
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.37
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.20
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.01
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.49
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.97
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.59
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.93
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.98
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.44
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.32
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.68
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.45
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.94
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.84
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.07
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.01
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.33
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.75
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.00
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.53
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.59
 p-value of test no 167                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.35
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.82
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.99
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.71
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.93
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.72
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.63
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.18
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.05
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.60
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.17
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.44
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.90
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.34
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.64
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.51
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.76
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.03
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.90
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.42
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.33
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000132514
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.15
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000126931
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:10.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97189906.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56916
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 12                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 15                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.13
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.98
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.22
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.95
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.94
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.78
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6828.20
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.21
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.72
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.64
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.91
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.25
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45413
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869413
   j =  1                              :        399909175
   j =  2                              :            45411
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908549
   j =  2                              :            45721
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-5
 p-value of test no 113                :    0.9901
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.15
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.93
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.70
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.07
 p-value of test no 122                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.11
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.47
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.75
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.72
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.43
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.36
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.24
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.93
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.99
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.99
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.02
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.30
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.91
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.79
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.75
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.92
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.11
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.10
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.85
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.96
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.90
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.21
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.77
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.57
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.50
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.53
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.76
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.14
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.77
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.85
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.20
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.13
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.91
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.73
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.41
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.96
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.44
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.78
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.98
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.27
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.02
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.74e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.99
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.43
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.78
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4303.53
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.61
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.98
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.15
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999963350
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.13
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999910079
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:13.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98205714.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56917
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.45
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.34
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.20
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.96
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.38
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.15
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.67
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.88
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 58                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 59                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.21
 p-value of test no 61                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.60
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.01
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.10
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.45
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908418
   j =  2                              :            45785
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46246
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870246
   j =  1                              :        399907511
   j =  2                              :            46240
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.35
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.14
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.15
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.16
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.42
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.02
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.91
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.00
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.83
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17598.48
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.97
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.19
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.33
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.55
 p-value of test no 149                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.09
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.06
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.56
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.91
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.49
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.50
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.69
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.11
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.95
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.80
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.57
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.34
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.88
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.66
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.56
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.03
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.14
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.81
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.55
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.89
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.51
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.11
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.98
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.49
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.02
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.48
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.08
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.28
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.11
 p-value of test no 198                :  6.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.61
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.80
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.45
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.21
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.05
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.78
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.04
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.63
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.28
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.79
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :  101.34
 p-value of test no 231                :  1.0e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999840056
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.96
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000071374
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:37:24.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  101  Run of bits, r = 0              1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99221522.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56918
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    3.24
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     262
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.31
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.05
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.94
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.53
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.23
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.58
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.10
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.93
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.82
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.66
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.18
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.20
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.93
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908360
   j =  2                              :            45817
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908039
   j =  2                              :            45973
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 108                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.61
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.97
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.22
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.05
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.61
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.68
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.87
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   71.48
 p-value of test no 133                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.43
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.23
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.62
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.58
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.19
 p-value of test no 147                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.45
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.82
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.93
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.04
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.17
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.72
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.39
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.57
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  575.86
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.49
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.35
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.30
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.34
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.86
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.70
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.43
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.94
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.37
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.49
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.39
 p-value of test no 171                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.93
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.36
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.22
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.72
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.75
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.46
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.04
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10221.78
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.18
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 216                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.90
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5090.04
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.41
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.53
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.24
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.67
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.69
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999967610
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.77
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000042727
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 248                :    0.85
 
 Sample variance                       :    2.20
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:17.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100237330.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56919
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 16                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.93
 p-value of test no 23                 :  3.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.41
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.42
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.16
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.43
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.57
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.31
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.58
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.55
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.00
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.40
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.40
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.74
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.52
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908544
   j =  2                              :            45725
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907827
   j =  2                              :            46079
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.63e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.90
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.07
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.68
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.08
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.62
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.62
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.82
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.82
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.49
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.72
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17740.46
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.68
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.22
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.28
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.62
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.12
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.70
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.52
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.59
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.09
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.50
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.98
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.18
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.79
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.95
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.39
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.04
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.43
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.50
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.76
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.89
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.33
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.09
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.73
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.36
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.39
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.05
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.00
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.94
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.19
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.90
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.18
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.23
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.38
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.36
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.21
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.09
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10261.72
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.18
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.65
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.74
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.38
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.40
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.20
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.85
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999921830
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.02
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999893822
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-3
 p-value of test no 236                :    0.9975
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:36:46.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101253138.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56920
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 11                 :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    4.49
 p-value of test no 39                 :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.36
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.36
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.18
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.37
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1526.15
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.36
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.12
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.51
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.20
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.99
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5265.42
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908110
   j =  2                              :            45939
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46295
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870295
   j =  1                              :        399907414
   j =  2                              :            46287
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.87
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.58
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.49
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.78
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   14.95
 p-value of test no 124                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.38
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.01
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.18
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.85
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.77
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17285.67
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.08
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.59
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.01
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.88
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.18
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.46
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.45
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.11
 p-value of test no 155                :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.39
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.08
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.17
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.69
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.77
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.57
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.85
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.34
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.91
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.26
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.11
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.51
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.71
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.79
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.73
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.03
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.72
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.49
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.28
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.11
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.10
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.85
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.25
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.30
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.23
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.86
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.00
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.59
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.42
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.16
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.26
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.95
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999980030
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.75
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999969920
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:18.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9991 
  64  WeightDistrib, r = 26           0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82083845.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56921
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 12                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.01
 p-value of test no 41                 :  9.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.48
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.20
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.22
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.26
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.32
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.99
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.32
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.52
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1325.50
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.90
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.19
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.30
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.45
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.33
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.15
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908047
   j =  2                              :            45975
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908680
   j =  2                              :            45654
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 108                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-4
 p-value of test no 112                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 114                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.99
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.92
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.57
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.59
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.36
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.27
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.80
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.42
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.05
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 139                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.46
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17631.53
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.53
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.18
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.77
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.51
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.53
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.03
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.62
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.26
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.48
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.55
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.54
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.00
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.71
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.89
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.60
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.47
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.83
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.43
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.66
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.08
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.03
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.29
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.67
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.62
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.79
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.41
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.30
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.70
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.64
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.65
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.53
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.60
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.53
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.40
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.13
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.10
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.19
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.59
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.48
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.26
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12033.97
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.40
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.39
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000112981
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.96
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999980045
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:10.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83787781.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56922
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    3.43
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.81
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.95
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.42
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.07
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.69
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.22
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.14
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.88
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.63
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.93
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.88
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.03
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.65
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.89
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.34
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907976
   j =  2                              :            46006
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908619
   j =  2                              :            45686
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.54
 p-value of test no 117                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.25
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.39
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.09
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.16
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.70
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.96
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.62
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.25
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.46
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.69
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.81
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.58
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.59
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.22
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.80
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.60
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.60
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.85
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.82
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.27
 p-value of test no 159                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.66
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.80
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.08
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.71
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.02
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.27
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.21
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.55
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.84
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.96
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.18
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.97
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.53
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.07
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.00
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.94
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.13
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.64
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.27
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.28
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.60
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.04
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.50
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5067.51
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.58
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.02
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11511.42
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12090.41
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.32
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999917258
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.27
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000161278
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.35
 p-value of test no 238                :    0.9907
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:24.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84869125.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56923
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 7                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.47
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.94
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.34
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.29
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.55
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.16
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.31
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.20
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.69
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.85
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.89
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.56
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.37
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.00
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908008
   j =  2                              :            45993
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908294
   j =  2                              :            45850
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.33
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.80
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.98
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.79
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.07
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.20
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.23
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.02
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.77
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.50
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.04
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.03
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.74
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.02
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.30
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.69
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.40
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.12
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.12
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.06
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.63
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.62
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.58
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.97
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.81
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.83
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.66
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.73
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.49
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.19
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.92
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.81
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.63
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.69
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.60
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.85
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.25
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.76
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.22
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.89
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.02
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.56
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.01
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.18
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.98
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.62
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000039781
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.80
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000132406
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    2.06
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 242                :  7.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 243                :    0.9946
 
 Sample variance                       :    2.80
 p-value of test no 244                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:36.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85852165.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56924
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    8.61
 p-value of test no 35                 :  6.6e-5    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.03
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.00
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.16
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.11
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.64
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.35
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.58
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.34
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.01
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.52
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.01
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.34
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.61
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.91
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.25
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908507
   j =  2                              :            45736
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908415
   j =  2                              :            45788
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.12
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.70
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.20
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.76
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.83
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.82
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.01
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
 p-value of test no 138                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 139                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 140                :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  189.12
 p-value of test no 141                :  5.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17767.98
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.62
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.18
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.48
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.43
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.40
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.23
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.13
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.55
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.83
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.11
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.91
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.38
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.08
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.92
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.88
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.23
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.47
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.45
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.26
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.71
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.04
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.74
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.76
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.99
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.81
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.42
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.66
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.89
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.10
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.85
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.12
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.07
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.26
 p-value of test no 216                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.27
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.57
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.33
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.75
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11518.51
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.60
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.32
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000066454
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.40
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000119599
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.047
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:24.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           6.6e-5
  72  Savir2                          5.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  92  HammingCorr, L = 30             0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86736901.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56925
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7553
 p-value of test no 18                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    3.71
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.81
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.46
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.12
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.68
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.77
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.96
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.15
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.72
 p-value of test no 58                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 60                 :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   11.39
 p-value of test no 61                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 62                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.22
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.79
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.67
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.34
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908264
   j =  2                              :            45868
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46326
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870326
   j =  1                              :        399907352
   j =  2                              :            46318
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 91                 :    0.9909
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.07
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.58
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.87
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.58
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.90
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.50
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.79
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.33
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.65
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.23
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.60
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17357.12
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.49
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.92
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.00
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.30
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.97
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.22
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.59
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.52
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.37
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.69
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.49
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.20
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.52
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.75
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.56
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.00
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.51
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.82
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.70
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.23
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.41
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.96
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.14
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.19
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.30
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.78
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.95
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.92
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.51
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.62
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.66
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.85
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.83
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.21
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.80
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.68
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.96
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.65
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.44
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.48
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.17
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.89
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999980255
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.90
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000058534
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:25.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  38  Run, r = 0                      0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87785477.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56926
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.19
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.64
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.04
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.13
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.36
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.00
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.40
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.67
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.96
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.36
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.44
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.35
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.86
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907777
   j =  2                              :            46107
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908181
   j =  2                              :            45896
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.05
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.51
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.58
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.28
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.46
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.47
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.41
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.43
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.21
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.05
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.86
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.47
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.02
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.00
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.72
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.81
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.00
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.29
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.58
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.66
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.72
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.17
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.56
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.27
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.34
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.51
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.11
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.92
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.01
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.00
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.88
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.08
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.74
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.85
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.08
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.40
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.31
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.50
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.21
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.03
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.18
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.99
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.80
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.78
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.15
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.60
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.67
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.54
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.87
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.01
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999792173
 
 Normal statistic for number of bits   :   -1.64
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.49
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999947144
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:22.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88801285.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56927
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.08
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.05
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.83
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.62
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   26.94
 p-value of test no 50                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.86
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.47
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.74
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.56
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.77
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.16
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.41
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.86
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.67
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.30
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908351
   j =  2                              :            45823
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908245
   j =  2                              :            45873
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.89
 p-value of test no 117                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.03
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.69
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.68
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.63
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.79
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.46
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.77
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.52
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.64
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.45
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.46
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17163.14
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.00
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.62
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.78
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.55
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.08
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.60
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.03
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.01
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.45
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.32
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  116.19
 p-value of test no 160                :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.59
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.49
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.40
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.75
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.75
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.20
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.36
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.38
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.71
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.15
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.75
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.83
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.20
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.43
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.10
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.48
 p-value of test no 196                :    0.9931
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.09
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.31
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.24
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.37
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.61
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 224                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4683.07
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.43
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.90
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.72
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.60
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999900578
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.91
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999982142
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 236                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:01.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9992 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89784325.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56928
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9972
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.71
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.26
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.51
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.30
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.36
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.70
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.08
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7251.25
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.64
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.10
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.68
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.73
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908589
   j =  2                              :            45695
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908283
   j =  2                              :            45851
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-3
 p-value of test no 97                 :    0.9990
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.88
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.43
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.84
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.76
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.84
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.99
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.12
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.99
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.97
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.36
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.43
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.52
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.52
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.80
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.63
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.64
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.20
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.14
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.30
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.30
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.52
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.48
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.69
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.34
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.06
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.63
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.34
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.21
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.29
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.34
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.95
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.07
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.92
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.92
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.29
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.86
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 201                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.22
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.60
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.08
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.85
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.100
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.33
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.04
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.82
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.97
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.76
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.17
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.74
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000100669
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.80
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999954803
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 236                :    0.9923
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:55.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91029509.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56929
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7110
 p-value of test no 15                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.48
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.11
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.03
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.38
 p-value of test no 51                 :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.54
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.15
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.95
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.46
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.02
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-3
 p-value of test no 59                 :    0.9987
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.28
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.85
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.79
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.12
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.19
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908300
   j =  2                              :            45844
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908646
   j =  2                              :            45671
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 98                 :    0.9911
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.90
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.02
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.42
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.82
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.55
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.96
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.64
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.46
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 140                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.71
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17707.86
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.53
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.41
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.19
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.25
 p-value of test no 149                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.72
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.25
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.85
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.70
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.06
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.16
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.30
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.93
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.54
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.67
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.89
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.53
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.32
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.97
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.05
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.47
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.00
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.44
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.97
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.40
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.62
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.34
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.84
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.49
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.83
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.96
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10229.79
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.69
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.05
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.89
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.56
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.72
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.74
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.48
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999951392
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.43
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999925907
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:18.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92045317.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56930
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.36
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.76
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.42
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.05
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.18
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.24
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.25
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.03
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.68
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.27
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.55
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   74.55
 p-value of test no 67                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.58
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908203
   j =  2                              :            45888
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908338
   j =  2                              :            45828
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.91
 p-value of test no 119                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.87
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.48
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.86
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.75
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.83
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.62
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.74
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 140                :  6.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   92.42
 p-value of test no 141                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.40
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.25
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.49
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.87
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.66
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.13
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.38
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.36
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.49
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.85
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.49
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.72
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.57
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.53
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.35
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.21
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.01
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.10
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.99
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.13
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.40
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.90
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.33
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.69
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.21
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.43
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.79
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.22
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.52
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.05
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.04
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.76
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.11
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.01
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.10
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.59
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.40
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.74
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.28
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.93
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.96
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.35
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.06
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.67
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999866498
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.41
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000076822
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-4
 p-value of test no 245                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.20
 p-value of test no 254                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:24.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92962821.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56931
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.92
 p-value of test no 34                 :  3.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.76
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.28
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.77
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.82
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.24
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.18
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.58
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.85
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.08
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.24
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.69
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.57
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.60
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.27
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45612
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869612
   j =  1                              :        399908777
   j =  2                              :            45610
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45529
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869529
   j =  1                              :        399908945
   j =  2                              :            45523
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 81                 :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.72
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.58
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.74
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.56
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.03
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.01
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.54
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.78
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.15
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.14
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.71
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.21
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17697.27
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.94
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.23
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.97
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.90
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.57
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.92
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.99
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.39
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.06
 p-value of test no 156                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.98
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.77
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.73
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.56
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.53
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.95
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.64
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.90
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.10
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.68
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.88
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.64
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.20
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.52
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.49
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.12
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5176.24
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.54
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.18
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.22
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.60
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.46
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.96
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.13
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10157.24
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.12
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.42e-3
 p-value of test no 224                :    0.9965
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4718.55
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.95
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.77
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.14
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.01
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.94
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000018580
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.10
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999984911
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:35.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93978629.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56932
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    3.47
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.98
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.94
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.76
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.88
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.91
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.91
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.32
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.39
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.84
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.09
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.61
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.07
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.85
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.21
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46181
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870181
   j =  1                              :        399907641
   j =  2                              :            46175
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908030
   j =  2                              :            45982
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 84                 :    0.9955
 
 Anderson-Darling statistic = A2       :    5.55
 p-value of test no 85                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.99
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.47
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.14
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.07
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.41
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.73
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.09
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.62
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.81
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.98
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.32
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.86
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.09
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.15
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.61
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.23
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.16
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.62
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.70
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.55
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.16
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.06
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.07
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.50
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.88
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.82
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.83
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.74
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.98
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.01
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.29
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.64
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.39
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.99
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.47
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.79
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.47
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.95
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.04
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 188                :    0.02
 
 Sample variance                       :    3.56
 p-value of test no 189                :  1.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.55
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
 p-value of test no 200                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.22
 p-value of test no 203                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.62
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.05
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.58
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.53
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.41
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.52
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.81
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.14
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.90
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.74
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000012487
 
 Normal statistic for number of bits   :   0.099
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.68
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999926729
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:06.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95059973.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56933
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 4                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4174
 p-value of test no 14                 :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.95
 p-value of test no 28                 :  9.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.62
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.16
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.64
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.97
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.02
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.78
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.72
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.73
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.19
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 59                 :    0.9952
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 60                 :  8.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.70
 p-value of test no 61                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.98
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.28
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.77
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45524
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869524
   j =  1                              :        399908956
   j =  2                              :            45516
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907765
   j =  2                              :            46110
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 94                 :    0.9907
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 103                :  1.7e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 104                :    0.9929
 
 Anderson-Darling statistic = A2       :    5.13
 p-value of test no 105                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.31
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.21
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.72
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.92
 p-value of test no 124                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.18
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.05
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.67
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.15
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.34
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.72
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.70
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.94
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.03
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.38
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.52
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.54
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.92
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.81
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.92
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.02
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.52
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.91
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.17
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.87
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.01
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.30
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.14
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.78
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.88
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.23
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.17
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.54
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.66
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.41
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.53
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.64
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.13
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.39
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-3
 p-value of test no 185                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.56
 p-value of test no 188                :  5.2e-3
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.08
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.04
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.37
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.58
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.86
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.17
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.97
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.80
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.60
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.48
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.14
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.72
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000190501
 
 Normal statistic for number of bits   :    1.51
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999950873
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:02.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96043013.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56934
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5549
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     660
 p-value of test no 31                 :  8.3e-3
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.40
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.65
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.50
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.15
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.15
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.14
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1612.32
 p-value of test no 56                 :  7.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.71
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.74
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.81
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.38
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908362
   j =  2                              :            45813
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908325
   j =  2                              :            45836
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 101                :  2.8e-4    *****
 
 Anderson-Darling statistic = A2       :    6.49
 p-value of test no 102                :  6.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.63
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.81
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.32
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.17
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.08
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.81
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.23
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.69
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.36
 p-value of test no 137                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.04
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17733.85
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.79
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.32
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.27
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.62
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.79
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.27
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.77
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.41
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.28
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.12
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.82
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.35
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.68
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.88
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.94
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.69
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.04
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.44
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.07
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.12
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.39
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.23
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.42
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.60
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.78
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.00
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.33
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.99
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.89
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.56
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.22
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.95
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.43
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.71
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4696.43
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.63
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.09
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.58
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.87
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.93
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999901127
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.86
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999977120
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.047
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:42.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      7.9e-4
  50  SampleProd, t = 8               6.0e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97058821.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56935
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.94
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    4.11
 p-value of test no 39                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.40
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.17
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.05
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.25
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.01
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.77
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.46
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.34
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.52
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7217.96
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.76
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.16
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.75
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.39
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.67
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908339
   j =  2                              :            45826
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908533
   j =  2                              :            45726
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.96
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.17
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.78
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.22
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.04
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.90
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.86
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.94
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.17
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.77
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.10
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.40
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.63
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.15
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.91
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.01
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.10
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.29
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.26
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.84
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.27
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.96
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.75
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.42
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.52
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.78
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.24
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.58
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.92
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.01
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.04
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.01
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.23
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.69
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.42
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.16
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.68
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.28
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.27
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.56
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.70
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.05
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999942512
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.11
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000119479
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:45.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98074629.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56936
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7519
 p-value of test no 20                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    3.24
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.42
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.21
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.78
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.32
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.60
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.59
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.83
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.71
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.04
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6891.08
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.48
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.64
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.39
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.41
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.16
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45595
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869595
   j =  1                              :        399908811
   j =  2                              :            45593
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907956
   j =  2                              :            46016
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.70
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.22
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.06
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.14
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.24
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.56
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.31
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.23
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17285.76
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.98
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.31
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.46
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.00
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.77
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.65
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.21
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.47
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.01
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.21
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.89
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.79
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.02
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.76
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.97
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.02
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.43
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.78
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.15
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.38
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.48
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.14
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.75
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.90
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.14
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.06
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.08
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.64
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.91
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.43
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.89
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 221                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5164.59
 p-value of test no 222                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.04
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.67
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4322.14
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12015.76
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.80
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.69
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999965864
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.00
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000132235
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    2.38
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:01.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99090437.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56937
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9939
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.53
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.84
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.29
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.92
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.61
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.87
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.34
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.84
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.39
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.22
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.24
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.22
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.49
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.50
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908850
   j =  2                              :            45569
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908036
   j =  2                              :            45970
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.02
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.57
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.03
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.93
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.85
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.08
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.65
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.74
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.40
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.82
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.20
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17379.77
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.30
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.51
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.29
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.81
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.43
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.09
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.60
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.76
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.37
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.97
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.46
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.56
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.61
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.06
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.91
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.23
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.57
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.47
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.02
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.73
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5232.32
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.45
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.04
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.86
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.41
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.34
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.06
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.47
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.85
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.02
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.92
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.73
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.53
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.45
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.21
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.43
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.09
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.25
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.42
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.62
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.48
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.06
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.51
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.14
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999968657
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.00
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999816281
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:39.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100073477.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56938
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.95
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.54
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.22
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.19
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.39
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.98
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.73
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.77
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.01
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.82
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.83
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.51
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908195
   j =  2                              :            45895
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908334
   j =  2                              :            45827
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9911
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.01
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.59
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.51
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.72
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.49
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.79
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.47
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.38
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.82
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.81
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.95
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.10
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.98
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.89
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.28
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.66
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.50
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.53
 p-value of test no 157                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.28
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.80
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.29
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.79
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.38
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.24
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.57
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.35
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.93
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.18
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.43
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.77
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.84
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.65
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.50
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.51
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.97
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.97
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.54
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.20
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.84
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.82
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.61
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.25
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.13
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.20
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.12
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.63
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.64
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.00
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.99
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.78
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000019612
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.28
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999982730
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 251                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:24.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101089285.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56939
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1224
 p-value of test no 11                 : 1 -  6.0e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334344
   j =  1                              :        599997552
   j =  2                              :             1224
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    6.74
 p-value of test no 24                 :  4.5e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     989
 p-value of test no 25                 :  1.8e-3
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.12
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.44
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.83
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.14
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.36
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.21
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.86
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.13
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.80
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.57
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.54
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.39
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907921
   j =  2                              :            46035
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45580
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869580
   j =  1                              :        399908847
   j =  2                              :            45566
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 76                 :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.58
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.71
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.36
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.66
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.92
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.70
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.94
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.79
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.54
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17794.71
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.26
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.56
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.46
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.82
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.28
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.33
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.12
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.68
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.93
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.40
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.33
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.75
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.48
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.38
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.82
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.75
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.67
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.21
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.57
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.29
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.47
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.93
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.26
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.57
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.36
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.82
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.06
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.41
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.12
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.22
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.14
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.45
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.81
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.38
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.14
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.58
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.24
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.29
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11576.47
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.71
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.48
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999775793
 
 Normal statistic for number of bits   :   -1.77
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.63
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000085984
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:59.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  6.0e-5
  22  ClosePairs mNP1, t = 3          4.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102072325.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56940
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9924
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.00
 p-value of test no 35                 :  9.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.54
 p-value of test no 48                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.14
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.09
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.99
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.39
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.01
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.62
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.22
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.58
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.28
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.33
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.55
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.43
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.71
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908125
   j =  2                              :            45933
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907985
   j =  2                              :            46003
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
 p-value of test no 76                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 87                 :    0.9965
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9939
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
 p-value of test no 101                :    0.9983
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.56
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.07
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.99
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.68
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.41
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.97
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.79
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.77
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.43
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.99
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.32
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.38
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.39
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.78
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.10
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.77
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.98
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.82
 p-value of test no 159                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.96
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.41
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.15
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.69
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.14
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.94
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.45
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.06
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.88
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.30
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.34
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.88
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.33
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.43
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.68
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.54
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.46
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.51
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.60
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.78
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.93
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.10
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.29
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.70
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.34
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.32
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.88
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12041.01
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.54
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000045187
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.29
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999967025
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:49:19.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82116614.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56941
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5573
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.44
 p-value of test no 29                 :  6.4e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.33
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.99
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.24
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.66
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.93
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.48
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.18
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.95
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6823.14
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.48
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.23
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.31
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.14
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.90
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46191
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870191
   j =  1                              :        399907622
   j =  2                              :            46183
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46126
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870126
   j =  1                              :        399907751
   j =  2                              :            46120
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.88
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.16
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.13
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.91
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.99
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.06
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.21
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.88
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.97
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.36
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9968
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.50
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.32
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.21
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.36
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.18
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.64
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.22
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.46
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.55
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.30
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.63
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.26
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.54
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.73
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.45
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.13
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.83
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.42
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.36
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.17
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.18
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.71
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.40
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.30
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.74
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5215.40
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.62
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.04
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.64
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.43
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.89
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.88
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.97
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.50
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.61
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.57
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.87
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.72
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.16
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.28
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.00
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000149239
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.10
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000126172
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:24.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP, t = 5           6.4e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83820550.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56942
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.45
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.94
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.81
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.84
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.26
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.98
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.43
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.69
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.57
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.23
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6836.54
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.44
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.54
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.51
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.53
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.32
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908010
   j =  2                              :            45992
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46126
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870126
   j =  1                              :        399907750
   j =  2                              :            46122
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-3
 p-value of test no 104                :    0.9983
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.65
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.30
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.09
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.33
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.65
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.43
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.45
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.28
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.35
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.30
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.05
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.97
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.30
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.78
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.60
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.62
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.20
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.41
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.16
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.45
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.88
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.92
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.96
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.15
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.39
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.92
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.07
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.02
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.13
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.57
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.89
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.77
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.53
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.85
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.96
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.59
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.60
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.29
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.01
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.71
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.27
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.28
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.52
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.59
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.76
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.92
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.74
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.96
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.71
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.77
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999897323
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.38
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999914102
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:02.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84836358.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56943
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 42                 :    0.9991    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.03
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.56
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.00
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.02
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  502.12
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.87
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.66
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.03
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.60
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.10
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.94
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908208
   j =  2                              :            45890
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908291
   j =  2                              :            45853
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  6.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.08
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.21
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.02
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.35
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.89
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.39
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.44
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.71
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.22
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.18
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17767.71
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.16
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.23
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.84
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.10
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.93
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.32
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.58
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.54
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.16
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.18
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.71
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.28
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.13
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.70
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.03
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.74
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.85
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.37
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.12
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.90
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.75
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.10
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.96
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.80
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.99
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.35
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.38
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.13
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.13
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.16
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.06
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.10
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.91
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.14
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5034.16
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.92
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.88
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.82
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.70
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.60
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.18
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999782039
 
 Normal statistic for number of bits   :   -1.72
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.01
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999909494
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:49.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9991 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85819398.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56944
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.77
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.34
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.36
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.75
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.26
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.94
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.92
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.65
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.49
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.91
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.30
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.56
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 62                 :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.50
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.39
 p-value of test no 66                 :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.84
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.59
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908259
   j =  2                              :            45869
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907850
   j =  2                              :            46069
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  3.9e-3
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.44
 p-value of test no 117                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.56
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.48
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.90
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.60
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.40
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   53.75
 p-value of test no 125                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.93
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 132                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.62
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.44
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.20
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.16
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.77
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.42
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.10
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.75
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.29
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.60
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.65
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.23
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.27
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.69
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.82
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.24
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.99
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.59
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.02
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.89
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.54
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.31
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.62
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.52
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.30
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.53
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.74
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.67
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.35
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.24
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9961
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.02
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.51
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.84
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.23
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9749.10
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 217                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.23
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.61
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.54
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.79
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.79
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.79
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.69
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999886583
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.52
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000068689
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.079
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 251                :    0.9917
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:56.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86769670.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56945
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.47
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.80
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.49
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.97
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.03
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.47
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.20
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.53
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.13
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.58
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.75
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.43
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.89
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.54
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908360
   j =  2                              :            45814
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908377
   j =  2                              :            45810
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.87
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.61
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.38
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.42
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.47
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.92
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.20
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.13
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.49
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.51
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.38
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   14.25
 p-value of test no 147                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.49
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.74
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.69
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.74
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.54
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.71
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.85
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.29
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.08
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.29
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.60
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.99
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.68
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.63
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.96
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.81
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.46
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.84
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.27
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.14
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.34
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.50
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.74
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.65
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.17
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.43
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.75
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.85
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.59
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.74
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.39
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.88
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9792.67
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.05
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.47
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.09
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.80
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.55
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.56
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999993779
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.92
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000028642
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:27.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       0.9993 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87719942.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56946
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1247
 p-value of test no 11                 :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334367
   j =  1                              :        599997506
   j =  2                              :             1247
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.38
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.35
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.80
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.12
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.25
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.14
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.86
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.22
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.94
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.19
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.80
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.98
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.36
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.84
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.10
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46351
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907299
   j =  2                              :            46349
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908576
   j =  2                              :            45709
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.44
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.48
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.67
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.70
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.22
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.12
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.60
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.072
 p-value of test no 134                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.77
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.38
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.96
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.89
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.57
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.18
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.48
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.99
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.54
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.02
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.46
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.08
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.22
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.91
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.16
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.42
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.02
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.71
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.79
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.18
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.38
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.52
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.06
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.91
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.35
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.76
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.31
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.55
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   58.24
 p-value of test no 176                :  4.7e-8    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.66
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.99
 p-value of test no 198                :    0.9983
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.83
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.07
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10320.22
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.07
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.03
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.90
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.26
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.83
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.75
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.64
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.13
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000061144
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.45
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999818666
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.089
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:11.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9993 
  80  LinearComp, r = 0              1 - eps1
  80  LinearComp, r = 0               4.7e-8
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88670214.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56947
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     541
 p-value of test no 31                 :    0.9923
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.93
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.96
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.85
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.68
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.91
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.65
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.90
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.96
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.27
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.17
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.92
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.94
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.85
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.05
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46206
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870206
   j =  1                              :        399907592
   j =  2                              :            46198
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907950
   j =  2                              :            46019
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.17
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.38
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.49
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.01
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.76
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.99
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.61
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.82
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.25
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.74
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.41
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.54
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.18
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.71
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.44
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.86
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.84
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.19
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.59
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.14
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.81
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.12
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.04
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.30
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.04
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.29
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.89
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.52
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.42
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.01
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.13
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.22
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.49
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.98
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.28
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.97
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.83
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.83
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.31
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10282.25
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.78
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.69
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.62
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.85
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.92
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.53
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.81
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.30
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000143479
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.89
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000106504
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.047
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:06.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89653254.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56948
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.17
 p-value of test no 23                 :  7.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.32
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    5.66
 p-value of test no 42                 :  1.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.16
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.15
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.85
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.63
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.98
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.72
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.70
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.62
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.74
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.59
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.50
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.01
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.54
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908308
   j =  2                              :            45843
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908060
   j =  2                              :            45967
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.73e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.41
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.11
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.71
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.70
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.90
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.68
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.98
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.15
 p-value of test no 129                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.01
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.40
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.29
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.86
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.08
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.39
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.74
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.96
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.75
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.93
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.73
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.54
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.33
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.48
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.64
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.46
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.14
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.93
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.00
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.16
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.04
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.21
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.55
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.25
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.28
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.08
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.82
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.23
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.98
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.46
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.95
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.59
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.02
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.30
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.89
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.98
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.30
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.92
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.38
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.16
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4326.18
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.10
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.87
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.11
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.84
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000114448
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.61
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000125020
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 236                :    0.9917
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 245                :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.45
 p-value of test no 248                :  7.1e-3
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:51.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9996 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90701830.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56949
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    3.03
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.89
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.80
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.91
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.38
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.97
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.90
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.90
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.17
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.68
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.97
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.40
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.55
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.47
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45553
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869553
   j =  1                              :        399908897
   j =  2                              :            45547
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908171
   j =  2                              :            45910
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.02
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.61
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.11
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.06
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.55
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.70
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.48
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.50
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.00
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 142                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17807.65
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.23
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.40
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.69
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.57
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.31
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.80
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.67
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.59
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.93
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.74
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.96
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.92
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.66
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.96
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.31
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.61
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.41
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.54
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.07
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.01
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.53
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.62
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.03
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.93
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.99
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.74
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.37
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.64
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.31
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.87
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.90
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.27
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.62
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.78
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.17
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.32
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.72
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.57
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.10
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.95
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999897722
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.43
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000039646
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:51.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91684870.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56950
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7516
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.60
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.78
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.10
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.19
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.78
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.04
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.02
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.34
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.81
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6907.38
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.21
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.06
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.22
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.36
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.23
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908559
   j =  2                              :            45719
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907931
   j =  2                              :            46027
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  8.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.11
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.59
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.97
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.83
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.51
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.92
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.92
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.46
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.23
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.26
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.34
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.82
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.91
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.66
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.88
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.03
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.69
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.27
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.90
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.34
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.53
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.45
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.11
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.70
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.72
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.02
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.55
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.39
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.92
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.58
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.77
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.35
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.75
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.20
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.14
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.72
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.95
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.60
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.68
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.54
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.54
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.59
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.70
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.51
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.10
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.45
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.79
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.79
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.25
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.10
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.27
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999905678
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   28.17
 p-value of test no 233                :    0.9986
 
 
 -----------------------------------------------
 Total number of bits:  8000096457
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 243                :    0.03
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:27.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92700678.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56951
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    4.26
 p-value of test no 27                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.18
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.09
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.92
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.29
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.08
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.22
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.64
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1342.78
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.35
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.07
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.07
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.12
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.40
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908638
   j =  2                              :            45675
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46223
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870223
   j =  1                              :        399907560
   j =  2                              :            46211
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.42
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.02
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.86
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.66
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.79
 p-value of test no 125                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.27
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.12
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.33
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17295.96
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.43
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.72
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.93
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.35
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.13
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.50
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.14
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.59
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.55
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.47
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.07
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.03
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.66
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.43
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.67
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.57
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.84
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.87
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.73
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.72
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.62
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.77
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.90
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.47
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.05
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.30
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.09
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.71
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.86
 p-value of test no 176                :    0.9964
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.95
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.41
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.65
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.44
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.41
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.82
 p-value of test no 216                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.79
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.17
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.88
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.54
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.89
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.75
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.94
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000090913
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.77
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000075667
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.88
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:07.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93716486.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56952
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4509
 p-value of test no 16                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.89
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.57
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.77
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.67
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.30
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.63
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.57
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.53
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.56
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.88
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.11
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.40
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.80
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.02
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.03
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45527
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869527
   j =  1                              :        399908950
   j =  2                              :            45519
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908531
   j =  2                              :            45730
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.97
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.49
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.76
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.02
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.71
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.27
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.03
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.97
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.40
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.18
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.22
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.43
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.73
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.84
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.51
 p-value of test no 150                :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.30
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.14
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.89
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.45
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.28
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.97
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.83
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.74
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.77
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.96
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.54
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.38
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.27
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.56
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.48
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.11
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.84
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.48
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.80
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.44
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.16
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.29
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.70
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.98
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.05
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.02
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.37
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.09
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.91
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.46
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 221                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.19
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.11
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.35
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.67
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.66
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.20
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.00
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999928229
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.32
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000057445
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.76e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:41.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94601222.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56953
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.36
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.04
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.46
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.30
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.68
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.76
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.27
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.51
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.93
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.53
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 63                 :    0.9967
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.20
 p-value of test no 65                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.89
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5230.28
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908325
   j =  2                              :            45833
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908524
   j =  2                              :            45735
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.76
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.23
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.44
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.83
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.13
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.29
 p-value of test no 124                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.96
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.63
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.71
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.90
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17624.08
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.57
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.90
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.36
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.76
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.11
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.48
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.85
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.38
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.55
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.22
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.11
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.40
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.36
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.24
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.89
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.65
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.10
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.80
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.20
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.92
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.08
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.47
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.81
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.13
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.59
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.10
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.45
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.25
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.26
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.80
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.29
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.11
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9781.21
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.45
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.31
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.11
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.66
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.50
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11547.81
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.62
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000029812
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.65
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000065935
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.86
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.089
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.090
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:44.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95617030.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56954
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.55
 p-value of test no 48                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.04
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.11
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.23
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.07
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.06
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.81
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.11
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.15
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.23
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.33
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.29
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.99
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908299
   j =  2                              :            45846
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908164
   j =  2                              :            45909
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.13
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.20
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.81
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.06
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.32
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.59
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.99
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.58
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.90
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17656.62
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.48
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.30
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.03
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.51
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.16
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.12
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.10
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.44
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.86
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.10
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.36
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.76
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.22
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.26
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.44
 p-value of test no 164                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.46
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.04
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.63
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.81
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.51
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.22
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.36
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.58
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.71
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.36
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.48
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.79
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.56
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.92
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.74
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.06
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.40
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.72
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.99
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.60
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.22
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.51
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.35
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.82
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999941036
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.72
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999857510
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:12.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96567302.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56955
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5623
 p-value of test no 13                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.34
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.45
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.81
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.46
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.86
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.60
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.29
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.45
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.69
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.69
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.04
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.66
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.36
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.21
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.58
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908354
   j =  2                              :            45814
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907885
   j =  2                              :            46053
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.02
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.77
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.11
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.12
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.57
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.64
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.57
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.19
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.41
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.45
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.28
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.61
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.09
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.66
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.91
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.93
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.21
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.60
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.59
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.49
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.04
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.72
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.30
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.71
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.40
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.39
 p-value of test no 161                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.76
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.08
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.81
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.65
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.65
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.18
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.75
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.57
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.03
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.07
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.24
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.92
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.02
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.80
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.44
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.88
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 186                :    0.9909
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-4
 p-value of test no 190                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.25
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.87
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.62
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.60
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.25
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.35
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.70
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.33
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.64
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.47
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.63
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000105670
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.04
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000008665
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:11.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97615878.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56956
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4161
 p-value of test no 16                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    3.36
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.39
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.97
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.04
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.06
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.97
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.21
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.61
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.80
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6799.67
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.33
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.08
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.57
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.84
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.60
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908452
   j =  2                              :            45771
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908493
   j =  2                              :            45752
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 86                 :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    5.02
 p-value of test no 88                 :  2.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9984
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.57e-4
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.53
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.96
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.76
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.92
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.49
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.96
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.09
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.81
 p-value of test no 133                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.35
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 138                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 139                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 140                :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  178.55
 p-value of test no 141                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.17
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.34
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.90
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.75
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.79
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.16
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.88
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.24
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.23
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.59
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.63
 p-value of test no 157                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.54
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.90
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.41
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.09
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.20
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.70
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.69
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.41
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.95
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.81
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.56
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.26
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.67
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.18
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.04
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.05
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.73
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.00
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.79
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.78
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.97
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.72
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.27
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.34
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.11e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.05
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.82
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.75
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.49
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.44
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.26
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.94
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000079999
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.81
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999987077
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:56.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98500614.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56957
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.97
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.18
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.88
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.05
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.07
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.31
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.46
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.52
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.12
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.65
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.43
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.88
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.91
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.37
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.37
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.74
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907749
   j =  2                              :            46118
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45327
 p-value of test no 71                 :    0.9951
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869327
   j =  1                              :        399909347
   j =  2                              :            45325
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.30
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.29
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.77
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.49
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.60
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.79
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.07
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.07
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.51
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.63
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.21
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.43
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.94
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.23
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.31
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.47
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.42
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.06
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.55
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.24
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.94
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.99
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.59
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.66
 p-value of test no 162                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.07
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.73
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.84
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.24
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.17
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.79
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.31
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.33
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.63
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.57
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.49
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.13
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.54
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.77
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.83
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.67
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.04
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.11
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9699.64
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.54
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.10
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.85
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.49
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.82
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.92
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.34
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999975329
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.69
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000012985
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    2.13
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:31.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99549190.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56958
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7079
 p-value of test no 18                 :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.27
 p-value of test no 34                 :  6.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.60
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.56
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.03
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.61
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.47
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.33
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.05
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.85
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.65
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.89
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.10
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.66
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.68
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.13
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.07
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908200
   j =  2                              :            45894
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908678
   j =  2                              :            45649
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 118                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.82
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.94
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.91
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.79
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.56
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   71.11
 p-value of test no 124                :  6.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.94
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.11
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.71
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.01
 p-value of test no 141                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.56
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.59
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.56
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.45
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.09
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.34
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.90
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.94
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.33
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.57
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.04
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.44
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.70
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.01
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.14
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.02
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.52
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.50
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.92
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.15
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.82
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.93
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.11
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.08
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.12
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.87
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.64
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.24
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.12
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.83
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.86
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10198.55
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4677.53
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.13
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3929.63
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.40
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.93
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.06
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.23
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999998768
 
 Normal statistic for number of bits   : -9.74e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.32
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000008557
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:32.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  64  WeightDistrib, r = 26           6.3e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100532230.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56959
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    3.43
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.60
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.04
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.84
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.67
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.59
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.44
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.76
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.36
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.48
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.29
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.39
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.78
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.05
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.11
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.37
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908474
   j =  2                              :            45757
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908031
   j =  2                              :            45980
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9989
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 118                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.61
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.17
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.14
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   11.22
 p-value of test no 125                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.54
 p-value of test no 129                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.04
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.69
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.16
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.39
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.80
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.75
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.26
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.04
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.01
 p-value of test no 152                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.82
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.96
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.84
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.36
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.77
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.84
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.52
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.12
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.18
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.36
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.82
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.17
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.67
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.72
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.68
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.98
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.96
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.43
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.81
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.85
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.92
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.36
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.95
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.04
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.78
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.59
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.13
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.86
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.50
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9749.27
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.21
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.78
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.28
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.61
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.73
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.21
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.29
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000023731
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.01
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999905534
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 235                :  9.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 236                :    0.9927
 
 Anderson-Darling statistic = A2       :    5.33
 p-value of test no 237                :  2.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.09
 p-value of test no 238                :    0.9990
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.086
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:08.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101548038.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56960
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 6                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 11                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5630
 p-value of test no 13                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.72
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.74
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.54
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.36
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.89
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.41
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.76
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.71
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.33
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.77
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.69
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.15
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.53
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.37
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46096
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907811
   j =  2                              :            46090
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907860
   j =  2                              :            46064
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 114                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.61
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.20
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.78
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.65
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.55
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.06
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.43
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.82
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.96
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.41
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.36
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.35
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.48
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.50
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.95
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.68
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.89
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.88
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.22
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.36
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.73
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.30
 p-value of test no 159                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.27
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.95
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.35
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.28
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.48
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.38
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.20
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.75
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.02
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.18
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.64
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.68
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.84
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.26
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.09
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.91
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.74
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.01
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.79
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.28
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.80
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.05
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10267.26
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.64
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.77
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.22
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.77
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.08
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.79
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000083179
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.71
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000088894
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    2.10
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:48.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82149383.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56961
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9965
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.53
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.24
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.64
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.67
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.35
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.24
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.96
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.07
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6896.45
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.00
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.41
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.83
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4958.93
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908851
   j =  2                              :            45570
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908095
   j =  2                              :            45942
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 91                 :    0.9954
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.87
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.54
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.77
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.77
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.51
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.84
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.97
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.08
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.015
 p-value of test no 134                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.35
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17270.98
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.94
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.60
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.71
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.21
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.68
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.02
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.56
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.70
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.22
 p-value of test no 159                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.24
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.45
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.36
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.64
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.08
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.44
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.01
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.65
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.05
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.47
 p-value of test no 169                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.55
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.76
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.52
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.60
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.73
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.69
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.16
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.11
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.90
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.74
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.63
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.13
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.98
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.86
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.97
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.52
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.59
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.57
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.33
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000033499
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.45
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999970340
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 240                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 242                :  3.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.85
 p-value of test no 243                :    0.9978
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:49.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         0.9995 
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83492890.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56962
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5220
 p-value of test no 13                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.18
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.15
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.88
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.11
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.20
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.29
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.32
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.00
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.94
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.34
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7170.48
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.16
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.36
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.79
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.51
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.72
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908207
   j =  2                              :            45892
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45500
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869500
   j =  1                              :        399909001
   j =  2                              :            45498
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 86                 :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
 p-value of test no 90                 :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 102                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.24
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.54
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.02
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.69
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.74
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.33
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.06
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.62
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.51
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.00
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.62
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.20
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.91
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.78
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.69
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.64
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.31
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.17
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.64
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.60
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.66
 p-value of test no 156                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.83
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.01
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.67
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.14
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.92
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.69
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.35
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.03
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.67
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.94
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.23
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.81
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.21
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.44
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.70
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.56
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.81
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.51
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.42
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.83
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.78
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.18
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.02
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.28
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.91
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.83
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.37
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12168.83
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.02
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.83
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999906884
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.43
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000044407
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    2.35
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:28.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84803610.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56963
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 4                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997193
   j =  2                              :             1402
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    3.88
 p-value of test no 32                 :  9.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    5.15
 p-value of test no 39                 :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.45
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.90
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.54
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.56
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.67
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.63
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.15
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.58
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.47
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.10
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.76
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.32
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908093
   j =  2                              :            45952
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908265
   j =  2                              :            45860
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-3
 p-value of test no 93                 :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 94                 :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    8.11
 p-value of test no 95                 :  1.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  4.6e-5    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.87
 p-value of test no 119                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.97
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.50
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.21
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.61
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.11
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.01
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.10
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.11
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17643.88
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.77
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.72
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.13
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.78
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.04
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.04
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.00
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.67
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.07
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.78
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.17
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.77
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.03
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.35
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.46
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.99
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.08
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.19
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.68
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.93
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.45
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.50
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.41
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.26
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.41
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.79
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.86
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.47
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.69
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.20
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.30
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.51
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10225.84
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.90
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 224                :  1.2e-3
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5142.01
 p-value of test no 226                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4402.09
 p-value of test no 227                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.73
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.29
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.91
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.62
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999996131
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.39
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000144550
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:21.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  4.6e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85721114.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56964
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    3.09
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.37
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.02
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.50
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.42
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.34
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.79
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.28
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.58
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.27
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.79
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908651
   j =  2                              :            45670
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908458
   j =  2                              :            45765
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 91                 :  7.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 92                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.80
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.63
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.41
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.93
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.09
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.00
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.89
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.50
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.54
 p-value of test no 133                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.21
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17357.65
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.42
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.01
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.37
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.93
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   74.55
 p-value of test no 151                :  1.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.11
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.46
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.15
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.72
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.97
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.55
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.10
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.30
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.13
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.18
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.36
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.91
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.09
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.44
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.93
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.05
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.72
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.80
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.92
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.34
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.24
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.84
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.84
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.85
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.78
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.36
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.79
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.07
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.40
 p-value of test no 198                :    0.9943
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.51
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.47
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.64
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10193.61
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.18
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.35
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.56
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.81
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.27
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.34
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.25
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000079441
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.54
 p-value of test no 233                :  3.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000051655
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:12.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      1.7e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86540314.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56965
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.72
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.60
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.95
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.89
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.54
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.82
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.83
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.62
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.15
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
 p-value of test no 62                 :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.95
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.83
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.67
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908119
   j =  2                              :            45933
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907863
   j =  2                              :            46061
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.03
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.86
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.95
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.05
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.22
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.27
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.61
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.09
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.43
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
 p-value of test no 138                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  177.98
 p-value of test no 141                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.28
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.65
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.34
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.22
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.17
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.75
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.51
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.08
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.07
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.09
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.02
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.20
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.66
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.51
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.54
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.02
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.06
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.55
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.27
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.56
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.76
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.17
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.72
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.17
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.23
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.94
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.95
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -401.91
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.11
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.84
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.73
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.78
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.29
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.40
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.84
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.07
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.21
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.66
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.29
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.88
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12047.69
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.77
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999850289
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.64
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999938729
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 240                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:46:03.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87654426.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56966
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.71
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.74
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.52
 p-value of test no 52                 :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.95
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.69
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.88
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.19
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.07
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.98
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.30
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.03
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.26
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.08
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908567
   j =  2                              :            45715
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908642
   j =  2                              :            45676
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.34
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.78
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.39
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.65
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.04
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.95
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.65
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.92
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 138                :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.88
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17415.00
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.41
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.74
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.91
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.28
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.77
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.27
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.47
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.71
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.97
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.67
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.34
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.22
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.28
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.69
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.02
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.61
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.15
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.49
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.59
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.15
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.87
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.84
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.89
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.99
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.13
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.20
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.33
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.74
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.92
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.43
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.48
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.29
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.06
 p-value of test no 216                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.17
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.74
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.86
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.01
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.06
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.02
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.30
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000087199
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.31
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000031735
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:55.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88735770.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56967
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.81
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   31.15
 p-value of test no 46                 :  5.8e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.24
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.23
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.22
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.73
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.84
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.37
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.16
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.38
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.57
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.45
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.00
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.54
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.44
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.00
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908426
   j =  2                              :            45784
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908178
   j =  2                              :            45908
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -2.20e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.17
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.90
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.20
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.21
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.47
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.33
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.85
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.87
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.40
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17636.05
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.65
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.01
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.64
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.74
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.89
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.63
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.25
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.07
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.25
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.08
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.74
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.17
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.98
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.67
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.73
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.23
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.48
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.34
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.73
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.90
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.77
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.58
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.79
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.29
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.58
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.38
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.13
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.51
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.45
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.06
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.06
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.98
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.97
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.04
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.94
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.41
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.43
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.75
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12132.46
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.44
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.48
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999990017
 
 Normal statistic for number of bits   :  -0.079
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.20
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999823727
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:47.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                5.8e-5
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89718810.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56968
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 8                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.85
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.03
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.14
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.45
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.26
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.72
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.76
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.21
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.31
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7350.26
 p-value of test no 57                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.49
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.83
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.59
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.70
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907780
   j =  2                              :            46101
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908322
   j =  2                              :            45833
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.26
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.30
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.98
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.21
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.08
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.03
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.00
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.28
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.13
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17729.29
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.41
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.72
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.18
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.09
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.38
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.62
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.77
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.11
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.50
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.42
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.08
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.05
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.59
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.63
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.24
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.23
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.34
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.19
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.95
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.71
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.18
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.08
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.89
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.46
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.05
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.02
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.93
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.07
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.80
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.81
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.40
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.11
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 206                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.70
 p-value of test no 207                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.89
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.48
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.23
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.57
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.87
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.29
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.41
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.15
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.93
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000107053
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.54
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999949367
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:49.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90734618.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56969
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.90
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.28
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.21
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.16
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.39
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.52
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6854.04
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.16
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.27
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.92
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.54
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.30
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908426
   j =  2                              :            45781
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907575
   j =  2                              :            46205
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
 p-value of test no 94                 :    0.9952
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9971
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.93
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.60
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.18
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.25
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.98
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.86
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.92
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.37
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
 p-value of test no 131                :    0.9964
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.86
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.69
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.40
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.13
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.72
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.81
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.25
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.90
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.32
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.94
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.10
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.67
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.50
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.53
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.33
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.95
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.89
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.64
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.74
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.12
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.11
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.56
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5203.15
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.28
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.48
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.17
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.96
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.13
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.64
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.73
 p-value of test no 175                :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.17
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.61
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.98
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.07
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.17
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.68
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.87
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.36
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.44
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.21
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.12
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.38
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.07
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.71
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.48
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.23
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.27
 p-value of test no 231                :  6.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000010273
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.29
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999878102
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.080
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.13
 p-value of test no 249                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:55.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91881498.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56970
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    3.71
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    3.22
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.27
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.62
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.43
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.60
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.71
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.73
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.27
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.25
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.66
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.71
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.26
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908101
   j =  2                              :            45942
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908218
   j =  2                              :            45885
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-4
 p-value of test no 112                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.52
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.31
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.28
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.87
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.64
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.58
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
 p-value of test no 130                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.58
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.85
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.08
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.37
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.97
 p-value of test no 147                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.54
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.41
 p-value of test no 149                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.48
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.00
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.32
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.23
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.96
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.04
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.53
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.57
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.48
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.26
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.42
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.67
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.66
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.07
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.13
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.18
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.23
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.00
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.16
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.38
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.42
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.62
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.99
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.86
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.32
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.81
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.43
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.72
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.62
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.34
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.00
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.47
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.87
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.96
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.05
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.45
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000138994
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.89
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999981683
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:12.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92897306.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56971
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 7                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    2.70
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.91
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.95
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.88
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.66
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.16
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.32
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.99
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.43
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.50
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.13
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.75
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.52
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.31
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.04
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.43
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908116
   j =  2                              :            45939
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908235
   j =  2                              :            45878
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.09
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.52
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.25
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.35
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.81
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.19
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.72
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.56
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.89
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.02
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17748.44
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.83
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.55
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.19
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.03
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.30
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.26
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.34
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.61
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.73
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.65
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.56
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.56
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.51
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.56
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.74
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.31
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.48
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.81
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.55
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.28
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.85
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.02
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.96
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.56
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.76
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.16
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.79
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.45
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.83
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.64
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.65
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.76
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.68
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.18
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.21
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.75
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.84
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.65
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.80
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.53
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.44
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.14
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.19
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.75
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000001681
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.49
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999983528
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:19.92
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93880346.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56972
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.79
 p-value of test no 28                 :  1.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    3.89
 p-value of test no 45                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.15
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.22
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.14
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.30
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.56
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.04
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.21
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.34
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.76
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.77
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.21
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.62
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908238
   j =  2                              :            45878
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908550
   j =  2                              :            45719
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9932
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.010
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.72
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.71
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.15
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.14
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.41
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.65
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.68
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.27
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.52
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.00
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.79
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.70
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.95
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.98
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.20
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.21
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.84
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.46
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.69
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.97
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.67
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.68
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.56
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.85
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.48
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.08
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.35
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.69
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.50
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.90
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.67
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.64
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5203.09
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.26
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.02
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.26
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.06
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.97
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.17
 p-value of test no 196                :    0.9970
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 199                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.79
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.76
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9651.78
 p-value of test no 211                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.35
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.70
 p-value of test no 216                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.11
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.92
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.70
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.50
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.11
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.71
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.15
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000236773
 
 Normal statistic for number of bits   :    1.87
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.20
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000005848
 
 Normal statistic for number of bits   :   0.046
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.091
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:10.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94928922.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56973
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7498
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7077
 p-value of test no 21                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.36
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    4.26
 p-value of test no 33                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.06
 p-value of test no 41                 :  8.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.31
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.13
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.28
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.08
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.90
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.33
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.02
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.20
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.11
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.71
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7234.11
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.17
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.05
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.30
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.97
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4823.44
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908458
   j =  2                              :            45765
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908201
   j =  2                              :            45895
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.30
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.71
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.22
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.43
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.83
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.36
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   14.50
 p-value of test no 136                :  7.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.20
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.96
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.32
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.14
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.92
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.71
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.08
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.70
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.36
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.86
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.20
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.32
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.40
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.94
 p-value of test no 161                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.88
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.99
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.60
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.39
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.10
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.51
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.80
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.15
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.72
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.89
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.48
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.02
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.27
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.57
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.27
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.86
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.40
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.50
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.26
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.29
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.10
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.15
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.51
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.99
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.85
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.46
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000118876
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.67
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999912182
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:22.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              7.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95911962.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56974
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 9                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4505
 p-value of test no 14                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.80
 p-value of test no 22                 :  3.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.97
 p-value of test no 34                 :  3.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.31
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.67
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.27
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.97
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.46
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.79
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1341.51
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.11
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.12
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.72
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.33
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.46
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45344
 p-value of test no 70                 :    0.9938
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869344
   j =  1                              :        399909318
   j =  2                              :            45332
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 107                :    0.9901
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 111                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.62
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.33
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.36
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.46
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.88
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.18
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.11
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.04
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.19
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.59
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.81
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.33
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.44
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.79
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.21
 p-value of test no 154                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.54
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.73
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.16
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.63
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.08
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.79
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.17
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.44
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.49
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.19
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.04
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.10
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.67
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.48
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.43
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.32
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.01
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.28
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.52
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.23
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.79
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.89
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.29
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.20
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.98
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.34
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.86
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.37
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.47
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.87
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.49
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.51
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.27
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.05
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.85
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999854390
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.76
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000002167
 
 Normal statistic for number of bits   :   0.017
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-3
 p-value of test no 250                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:03.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96927770.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56975
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.45
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.59
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.13
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.41
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.62
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.11
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.70
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.41
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.10
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.40
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.61
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.30
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.09
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.40
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.96
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908233
   j =  2                              :            45873
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908336
   j =  2                              :            45826
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.14e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.46
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.00
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.93
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.57
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.28
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.16
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.80
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.37
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.23
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.88
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.20
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.18
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.55
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.52
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.08
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.35
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.73
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.95
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.97
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.57
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.24
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.09
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.32
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.14
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.35
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.22
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.49
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.46
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.86
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.11
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.00
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.43
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.32
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.70
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.40
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.42
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.33
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.82
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.10
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.68
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.09
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.64
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.93
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.68
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.48
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.27
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.24
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.72
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.37
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.32
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.29
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.35
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999990500
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.86
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999963842
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9942
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.072
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.045
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:57.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97943578.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56976
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.96
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.90
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.79
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.25
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.59
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.71
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.56
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.70
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.13
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.86
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.50
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.28
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.00
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.95
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908351
   j =  2                              :            45823
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908164
   j =  2                              :            45915
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.88
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.56
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.01
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.94
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.01
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.20
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.45
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.69
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.83
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.47
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.71
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.13
 p-value of test no 148                :  2.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.45
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.60
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.51
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.67
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.68
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.76
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.70
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.34
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.31
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.69
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.77
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.23
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.08
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.31
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.25
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.34
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.01
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.41
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.56
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.58
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.14
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.90
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.72
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.40
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.79
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.41
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.57
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.13
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.41
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.67
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.84
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.92
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.68
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.66
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.03
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.22
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.69
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.85
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12053.32
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.53
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.78
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000004210
 
 Normal statistic for number of bits   :   0.033
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.42
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999988604
 
 Normal statistic for number of bits   :  -0.090
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:54.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98992154.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56977
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7117
 p-value of test no 21                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.09
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.23
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.07
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.87
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.35
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.72
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.98
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.62
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.25
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.67
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.79
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.37
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.17
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.35
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.90
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907981
   j =  2                              :            46005
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908569
   j =  2                              :            45711
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 86                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.24
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.56
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.83
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.20
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.92
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.63
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.35
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.73
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.67
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.29
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.02
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17157.97
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.93
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.70
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.91
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.46
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.71
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.22
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.10
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.93
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.00
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.21
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.26
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.15
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.98
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.92
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.01
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.71
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.60
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.53
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.16
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.08
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.45
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4755.69
 p-value of test no 168                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.83
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.25
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.72
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.67
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.47
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.29
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.29
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.17
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.54
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.88
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.30
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.29
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.11
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.47
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.97
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.86
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.60
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.26
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.07
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11639.14
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.54
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999966173
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.59
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000140497
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:21.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100007962.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56978
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.89
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.05
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.99
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.08
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.20
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.47
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.68
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.78
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  282.51
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.98
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.69
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.84
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.13
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.20
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.68
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.42
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.11
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908136
   j =  2                              :            45923
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907852
   j =  2                              :            46074
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.07
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.75
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.07
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.68
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.59
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.05
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.54
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.29
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.64
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.07
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.47
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.68
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.26
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.05
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.88
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.38
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.24
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.58
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.17
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.36
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.43
 p-value of test no 159                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.01
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.65
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.25
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.63
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.56
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.35
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.75
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.51
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.31
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.39
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.30
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.99
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.58
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.68
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.15
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.44
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.04
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.23
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.82
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 186                :    0.9971
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.79
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.13
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.35
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.97
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9761.23
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.98
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.12
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.48
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.42
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.17
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.70
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.42
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.64
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000161989
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.26
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999972284
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:16.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 101056538.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56979
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.44
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.83
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.65
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.31
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.34
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.44
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.34
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.89
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.58
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.92
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.44
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.50
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.51
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907953
   j =  2                              :            46019
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908390
   j =  2                              :            45802
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 83                 :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 86                 :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.71
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.26
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.52
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.96
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.75
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.51
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.48
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.05
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.32
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.35
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.41
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.61
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.93
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.48
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.20
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.87
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.74
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.16
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.78
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.47
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.30
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.94
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.13
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.32
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.69
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.78
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.41
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.42
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.85
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.41
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.91
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.69
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.59
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.16
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.93
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.43
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.59
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.51
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.58
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.28
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.31
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.73
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.39
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.94
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4640.43
 p-value of test no 222                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.76
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.16
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.27
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.73
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.00
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.38
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000099817
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.85
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000125980
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 238                :    0.9939
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 248                :    0.12
 
 Sample variance                       :    2.25
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:21.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 102006810.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56980
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.30
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     341
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.99
 p-value of test no 41                 :  9.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.53
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.07
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.54
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.60
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.81
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.49
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.91
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.34
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.05
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.96
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.25
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.01
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.47
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908284
   j =  2                              :            45852
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45602
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908798
   j =  2                              :            45598
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.31e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.25
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.73
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.55
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.40
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.62
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.97
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.07
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.76
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.03
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.78
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.48
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.08
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.11
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.41
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.77
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.30
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.37
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.35
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.66
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.96
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.76
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.64
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.30
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.61
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.56
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.06
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.26
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.87
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.63
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.73
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.57
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.57
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.10
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.71
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.35
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.34
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.38
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.37
 p-value of test no 176                :  6.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.06
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.44
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.63
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.43
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.57
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.17
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.27
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.35
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.69
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.24
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.10
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.26
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.25
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.28
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999908477
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.59
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999834128
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.93
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9919
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:48:57.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 82182152.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56981
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 35                 :    0.9979
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.26
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.27
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.90
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.87
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.80
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.46
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1548.44
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7182.82
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.88
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.13
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.90
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5235.16
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907734
   j =  2                              :            46127
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908437
   j =  2                              :            45774
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.70
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.86
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.98
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.00
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.59
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.43
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.80
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.45
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.59
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.27
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.72
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.12
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.92
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.21
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.01
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.18
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.88
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.63
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.18
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.63
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.63
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.00
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.30
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.65
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.65
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.06
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.29
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.71
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.48
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.41
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.88
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.47
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.24
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.24
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.37
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.18
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.69
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.18
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.78
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.25
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.38
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.91
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.43
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 204                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.93
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.07
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.83
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.53
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.63
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.12
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.96
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.66
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.16
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.32
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000051067
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999928502
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 248                :    0.03
 
 Sample variance                       :    2.28
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:47:01.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 83591176.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56982
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.89
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.54
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.94
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.47
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.45
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.30
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.52
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.78
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.84
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.41
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.05
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.57
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.18
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.74
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4932.27
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46334
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870334
   j =  1                              :        399907337
   j =  2                              :            46324
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908593
   j =  2                              :            45696
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.74
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.64
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.50
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.59
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.95
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.05
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.92
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.75
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.45
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.50
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.76
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.90
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.53
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.56
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.31
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.27
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.81
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.65
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.95
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.48
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.52
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.62
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  586.03
 p-value of test no 158                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.33
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.58
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.00
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.63
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.72
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.75
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.21
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.26
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.69
 p-value of test no 167                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.49
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.57
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.55
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.29
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.44
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.58
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.97
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.87
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.73
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.10
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.35
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.31
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.42
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.29
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.20
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10245.75
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.91
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.58
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.27
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.95
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.22
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.76
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.09
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999897782
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.73
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000051820
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:45:41.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 84672520.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56983
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     262
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.57
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.95
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.69
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.02
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.83
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.16
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.54
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.89
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.05
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.97
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.56
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.71
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908672
   j =  2                              :            45658
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45503
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869503
   j =  1                              :        399908997
   j =  2                              :            45497
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.93
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.35
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.35
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.10
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.94
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.82
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.76
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.00
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.51
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.67
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.27
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.48
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.96
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.72
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.88
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.81
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.52
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.49
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.04
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.69
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.64
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.31
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.54
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.72
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.74
 p-value of test no 167                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.94
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.33
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.08
 p-value of test no 170                :    0.9932
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.82
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.67
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.50
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.35
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.96
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.42
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.80
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.80
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.55
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 186                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.35
 p-value of test no 188                :  9.4e-3
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.24
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.72
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.87
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.41
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.55
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.03
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.23
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.97
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.82
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.95
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.84
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.04
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999969926
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.33
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000015508
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:43.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 85426184.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56984
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    3.61
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.92
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.18
 p-value of test no 40                 :  7.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.81
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.87
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.41
 p-value of test no 51                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.31
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.72
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.50
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.01
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6843.96
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.80
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.90
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.70
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.85
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.92
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907931
   j =  2                              :            46030
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908346
   j =  2                              :            45824
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.83
 p-value of test no 119                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.45
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.08
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.99
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.65
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.53
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.66
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.55
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17516.72
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.90
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.27
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.85
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.87
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.02
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.28
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.01
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.64
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.31
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.43
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.17
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.24
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.53
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.15
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.41
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.12
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.13
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.48
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.49
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.00
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.39
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.22
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.50
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.48
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.71
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.95
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.58
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.94
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.72
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.43
 p-value of test no 198                :    0.9939
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.85
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.82
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.40
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.70
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 220                :    0.9957
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4675.94
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.99
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.55
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.93
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.65
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.43
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.06
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999921569
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.73
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999855338
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:35.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 86114312.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56985
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 4                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5267
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.08
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.13
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.42
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.88
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.89
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.07
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.92
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.86
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.05
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.12
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.54
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.74
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4887.26
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908071
   j =  2                              :            45960
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908354
   j =  2                              :            45817
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.09
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.76
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.14
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.63
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.99
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.98
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.79
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.02
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.51
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.97
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.75
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.16
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.63
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.47
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.04
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.66
 p-value of test no 153                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.41
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.97
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.14
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.45
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.38
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.12
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.20
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.38
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.05
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.28
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.54
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.96
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.15
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.62
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.71
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.14
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.34
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.79
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.79
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.79
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.95
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.28
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.31
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.12
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 204                :  1.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
 p-value of test no 205                :    0.9986
 
 Anderson-Darling statistic = A2       :    7.14
 p-value of test no 206                :  3.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  133.71
 p-value of test no 207                : 1 -  9.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.02
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.85
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.63
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.13
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.03
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.64
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.88
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.62
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000221656
 
 Normal statistic for number of bits   :    1.75
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.83
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000009964
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:43:53.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  89  PeriodsInStrings, r = 20       1 -  9.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 87130120.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56986
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.63
 p-value of test no 23                 :  4.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    3.46
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.67
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.64
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.85
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.70
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.71
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.32
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.55
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.24
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.82
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.46
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.22
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.60
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.39
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.81
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.19
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.67
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.04
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908926
   j =  2                              :            45534
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908666
   j =  2                              :            45664
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-4
 p-value of test no 79                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 80                 :  1.8e-3
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 81                 :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  5.1e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 84                 :    0.9929
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.98
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.93
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.08
 p-value of test no 123                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.73
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.44
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.28
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.98
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.06
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.66
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.12
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.51
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.88
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.37
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.44
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.09
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.90
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.54
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.16
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.77
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.86
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.83
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.78
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.56
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.06
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.73
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.72
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.39
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.28
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.44
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.75
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.63
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.40
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.27
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.77
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.13
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.79
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.39
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.71
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.19
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.15
 p-value of test no 184                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.76
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.92
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.80
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.59
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.31
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.08
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.47
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.80
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.80
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12086.80
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.60
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.95
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000017644
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.74
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999834593
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 236                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:44:08.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  5.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 88113160.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56987
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 11                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    4.16
 p-value of test no 27                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.70
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.35
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.06
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.56
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.15
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.01
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.63
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.94
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.33
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.59
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.51
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.10
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.25
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908299
   j =  2                              :            45843
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908522
   j =  2                              :            45736
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.23
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.15
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.42
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.54
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.11
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.91
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.99
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.79
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.42
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.65
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.65
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.57
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.75
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.56
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.04
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.63
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.73
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.71
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.47
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.66
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.62
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.83
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.36
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.84
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.42
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.34
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.42
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.69
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.37
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.67
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.11
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.67
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.65
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.80
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.90
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.15
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.11
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.44
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 208                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10290.44
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.16
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.30
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.98
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.37
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.25
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.07
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.18
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.11
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.56
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999835463
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.73
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999986069
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:55.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 89194504.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56988
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.07
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.32
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.31
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  277.51
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.25
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.22
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.05
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.78
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.71
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.85
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.81
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.49
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908430
   j =  2                              :            45779
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907756
   j =  2                              :            46113
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.26
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.74
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.92
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.89
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.78
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.07
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.49
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.37
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.76
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.19
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.92
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.27
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.13
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.05
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.96
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.35
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.12
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.18
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.26
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.49
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.50
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.50
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.98
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.38
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.10
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.92
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.91
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.20
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.51
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.66
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.30
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.95
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.86
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.62
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.25
 p-value of test no 170                :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.73
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.22
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5228.04
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.49
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.92
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.51
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.70
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.51
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.38
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.66
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.92
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.66
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.92
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.77
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.91
 p-value of test no 217                : 1 -  4.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 219                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5187.92
 p-value of test no 222                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.33
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.38
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.10
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.63
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.03
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.30
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000065221
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.86
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999844808
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:05.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  93  HammingCorr, L = 300           1 -  4.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 90177544.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56989
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.98
 p-value of test no 23                 :  3.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.52
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.58
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.29
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.78
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  282.68
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.51
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.46
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.29
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.10
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.74
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.05
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.02
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907865
   j =  2                              :            46063
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908536
   j =  2                              :            45726
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-3
 p-value of test no 98                 :    0.9968
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.21
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.22
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.21
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.22
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.34
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.35
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.84
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.65
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.30
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17274.88
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.25
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.19
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.37
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.41
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.64
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.93
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.72
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.50
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.70
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.58
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.37
 p-value of test no 157                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.69
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.62
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.85
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.49
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.39
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.38
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.31
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.31
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.12
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.72
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.58
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.81
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.01
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.39
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.59
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.94
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.59
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.17
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.44
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.83
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.36
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.28
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.11
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.88
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.57
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.06
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3786.27
 p-value of test no 227                : 1 -  9.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.77
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.55
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.84
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.10
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999974882
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.08
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000036475
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.97
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:50.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  97  HammingIndep, L=300, r=0       1 -  9.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 91193352.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56990
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.13
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.90
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.19
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.65
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.36
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.26
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.55
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.77
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.20
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.68
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.12
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.57
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45542
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908920
   j =  2                              :            45534
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46477
 p-value of test no 71                 :  2.7e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870477
   j =  1                              :        399907048
   j =  2                              :            46473
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 95                 :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.39
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.78
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.72
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.57
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.06
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.84
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.93
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.01
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.14
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.90
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.65
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.48
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.29
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.65
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.53
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.74
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.46
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.84
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.63
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.38
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.59
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.43
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.05
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.64
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.15
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.34
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.12
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.22
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.47
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.99
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.47
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.09
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.65
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.24
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.26
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.56
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.40
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.72
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.37
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.55
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.48
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.92
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.29
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 219                :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4700.79
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.82
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3948.51
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.41
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.36
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11526.04
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.39
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999894989
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.50
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999985412
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:24.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 92110856.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56991
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 10                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.32
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.36
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.21
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.76
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.19
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.50
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.92
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.57
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.29
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.06
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.60
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.16
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.46
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 60                 :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.44
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.85
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.74
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.33
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907992
   j =  2                              :            45998
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907605
   j =  2                              :            46190
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 103                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 105                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 107                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.40
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.49
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.03
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.82
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.84
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.42
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.47
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.90
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.54
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.92
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17342.43
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.60
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.24
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.69
 p-value of test no 149                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.62
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.98
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.02
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.61
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.60
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.39
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.61
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.76
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.91
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.21
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.48
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.32
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.96
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.38
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.36
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.79
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.23
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.33
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.26
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.78
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.56
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.28
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.96
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.25
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.93
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.18
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.53
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.27
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-4
 p-value of test no 180                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.35
 p-value of test no 183                :  9.3e-3
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.89
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.17
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.04
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.53
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.04
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.91
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.74
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.34
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.15
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.10
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.68
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000026332
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.88
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999947723
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:42:16.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 93323280.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56992
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    7.14
 p-value of test no 35                 :  3.1e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.30
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.85
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.32
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.78
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.95
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.29
 p-value of test no 52                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.60
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.66
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.77
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.41
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.23
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.07
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.23
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.68
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.11
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908539
   j =  2                              :            45726
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908011
   j =  2                              :            45990
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.88
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.28
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.08
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.20
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.29
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.07
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.73
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.83
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.35
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.09
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.26
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.02
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.20
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.40
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.84
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.97
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.38
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.70
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.29
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.12
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.64
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.45
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.13
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.14
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.24
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.50
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.88
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.14
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.55
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.54
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.54
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.95
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.71
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.79
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  470.21
 p-value of test no 174                :  8.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.71
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.34
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.82
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.26
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.62
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.42
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.56
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.16
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.85
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.28
 p-value of test no 218                :  5.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.14
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.64
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.92
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4280.14
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.19
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.51
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.27
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999978467
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.39
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999942968
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:55.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           3.1e-4
  79  RandomWalk1 R (L=10000, r=15)   8.5e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  94  HammingCorr, L = 1200           5.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 94306320.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56993
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 8                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 12                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 35                 :    0.9972
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.12
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.85
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.39
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.15
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.06
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.37
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.37
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.42
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.29
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.79
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.50
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.83
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.85
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908066
   j =  2                              :            45967
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45552
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908901
   j =  2                              :            45542
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.74
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.57
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.41
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.31
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.10
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.56
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.56
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.97
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.22
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.55
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.18
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.56
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.11
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.63
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.15
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.14
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.61
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.22
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.38
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.03
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.84
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.22
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.55
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.44
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.72
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.94
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.95
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.02
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.88
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.82
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.45
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.97
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.09
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.94
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.12
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.33
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.22
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.56
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.47
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.69
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.96
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.33
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.39
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.02
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.38
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.41
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.18
 p-value of test no 217                :  7.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 221                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.12
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.62
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.71
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.24
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11682.40
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.89
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.75
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000067804
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.39
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000002908
 
 Normal statistic for number of bits   :   0.023
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:28.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  93  HammingCorr, L = 300            7.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 95354896.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56994
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4482
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.40
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.55
 p-value of test no 47                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.61
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.39
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.47
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.36
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.28
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.43
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.01
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.77
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1327.12
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.98
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.70
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.25
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.53
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.84
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.51
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45321
 p-value of test no 70                 :    0.9955
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869321
   j =  1                              :        399909361
   j =  2                              :            45315
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907589
   j =  2                              :            46198
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.80
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.41
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.23
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.05
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.62
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.01
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.87
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 130                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.22
 p-value of test no 133                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.39
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17516.49
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.91
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.84
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.84
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.20
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.20
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.23
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.09
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.09
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.33
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.87
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.61
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.67
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.49
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.81
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.69
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.90
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.48
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.21
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.25
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.96
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.28
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.53
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.34
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.69
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.61
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.07
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.92
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.30
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.16
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.50
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.78
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.07
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.41
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.53
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.83
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.58
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.10
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3963.21
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.27
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.52
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.33
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.00
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000115870
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.37
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999921059
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.80e-4
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:14.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 96305168.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56995
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 9                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.26
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.79
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.03
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.41
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.09
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.38
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.80
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.42
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.40
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.79
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.97
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.18
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.65
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908531
   j =  2                              :            45724
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908490
   j =  2                              :            45749
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.89
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.60
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.74
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.43
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.50
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.46
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.69
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.85
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.82
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.35
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.26
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.67
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.14
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.02
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.04
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.29
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.90
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.64
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.35
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.74
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.07
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.56
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.06
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.99
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.07
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.00
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.57
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.78
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.25
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.20
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.65
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.94
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.03
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.48
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.57
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.61
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.06
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.10
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.37
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.53
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.61
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.57
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -403.03
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 181                :    0.9942
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.78
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.43
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.74
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10317.62
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.34
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.10
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.15
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.39
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.62
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.88
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.58
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.71
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000069556
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.00
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999946010
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 238                :    0.9931
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 240                :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 241                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.54
 p-value of test no 243                :  5.5e-3
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    2.30
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:41:20.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 97353744.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56996
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.99
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.39
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.67
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.09
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.48
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.58
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.25
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 60                 :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.50
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.28
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.08
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.95
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.11
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907956
   j =  2                              :            46019
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908715
   j =  2                              :            45638
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.30
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.35
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.98
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.16
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.10
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.48
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.88
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.37
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.61
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.52
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.88
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.21
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.34
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.03
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.26
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.27
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.69
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.17
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.34
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.49
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.97
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.41
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.08
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.01
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.17
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.56
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.67
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.01
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.35
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.32
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.45
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.08
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.89
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.59
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.97
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.22
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.42
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.97
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.93
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.42
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.16
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.69
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.10
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.13
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
 p-value of test no 224                :    0.9920
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.93
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.29
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4323.68
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12139.77
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.04
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.91
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000033112
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.71
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000091561
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:40:21.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 98369552.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56997
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1503
 p-value of test no 12                 :  1.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334623
   j =  1                              :        599996994
   j =  2                              :             1503
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7499
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.39
 p-value of test no 47                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.00
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.45
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.38
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.29
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.55
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.60
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.50
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.94
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.01
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.88
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908348
   j =  2                              :            45817
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907966
   j =  2                              :            46011
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 86                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    5.77
 p-value of test no 88                 :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9989
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.28
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.22
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.76
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.69
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.67
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.85
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.29
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.76
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
 p-value of test no 138                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.74
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.76
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.72
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.71
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.29
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.24
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.06
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.34
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.87
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.82
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.80
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.61
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.37
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.14
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.89
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.85
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.08
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.47
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.40
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.23
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.40
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.11
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.58
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.41
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.39
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.31
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.37
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.40
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.48
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.56
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.93
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.67
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.44
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.56
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.39
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.57
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.27
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.35
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.23
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12213.23
 p-value of test no 229                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.51
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.19
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000076957
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.52
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000097573
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.17
 p-value of test no 239                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 250                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 251                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    5.26
 p-value of test no 252                :  2.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.13
 p-value of test no 253                :  8.8e-4    *****
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:50.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.1e-4
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  106  AutoCor, d=3, r=27              8.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 99352592.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56998
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.34
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.30
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.63
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.26
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.05
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.43
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.03
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.00
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.75
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1553.21
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.84
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.80
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.75
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.80
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.84
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907846
   j =  2                              :            46071
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907705
   j =  2                              :            46143
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-3
 p-value of test no 103                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.17
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.03
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.35
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.39
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.40
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.26
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.21
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.29
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.55
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.30
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.41
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.98
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.53
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.06
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.59
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.81
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.57
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.50
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.04
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.39
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.46
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.01
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.41
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.63
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.07
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.87
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.48
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.80
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.24
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.21
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.78
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.08
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.45
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.89
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.00
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.72
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.64
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.52
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.43
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.79
 p-value of test no 176                :    0.9969
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.87
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.71
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.45
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.43
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.60
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.16
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10251.41
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.37e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.28
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.29
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.37
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.05
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.37
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.91
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.26
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000064318
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.46
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999978515
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:39:01.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
 Server wird beendet - Lösche Semaphor 100335632.
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 56999
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.47
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.46
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.71
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.11
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.04
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.45
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.96
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.75
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.52
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.53
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.07
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.94
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.11
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.76
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.89
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.43
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.98
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908342
   j =  2                              :            45820
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907748
   j =  2                              :            46120
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9921
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.17
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.90
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.64
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.20
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.91
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.56
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.57
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.21
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.18
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.22
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.12
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.29
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.84
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.21
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.53
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.08
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.36
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.42
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.15
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.32
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.60
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.07
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.07
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.10
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.13
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.15
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.38
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.92
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.65
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.67
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  263.48
 p-value of test no 170                :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.42
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.43
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.04
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.29
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.97
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.49
 p-value of test no 177                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -402.67
 p-value of test no 179                : 1 - eps1    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9926
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.00
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 202                :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  259.42
 p-value of test no 203                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.63
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.27
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.07
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.23
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.87
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.72
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.53
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.33
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.23
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.30
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999996209
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.13
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999965642
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 MT19937
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        MT19937
  Number of statistics:  160
  Total CPU time:   02:38:14.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 - eps1
  81  LinearComp, r = 29             1 - eps1
  ----------------------------------------------
  All other tests were passed
 
 
 
 
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